Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems
Introductory textbook from which students can approach more advance topics relating to finite difference methods.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia , PA
Society for Industrial and Applied Mathematics
2007
|
| Schriftenreihe: | Other titles in applied mathematics
98 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Introductory textbook from which students can approach more advance topics relating to finite difference methods. |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XV, 341 S. graph. Darst. |
| ISBN: | 9780898716290 |
Internformat
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| 100 | 1 | |a LeVeque, Randall J. |d 1955- |e Verfasser |0 (DE-588)112053688 |4 aut | |
| 245 | 1 | 0 | |a Finite difference methods for ordinary and partial differential equations |b steady-state and time-dependent problems |c Randall J. LeVeque |
| 264 | 1 | |a Philadelphia , PA |b Society for Industrial and Applied Mathematics |c 2007 | |
| 300 | |a XV, 341 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Other titles in applied mathematics |v 98 | |
| 500 | |a Includes bibliographical references and index | ||
| 520 | 3 | |a Introductory textbook from which students can approach more advance topics relating to finite difference methods. | |
| 650 | 4 | |a Finite differences | |
| 650 | 4 | |a Differential equations | |
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Datensatz im Suchindex
| _version_ | 1804136587861164033 |
|---|---|
| adam_text | Titel: Finite difference methods for ordinary and partial differential equations
Autor: LeVeque, Randall J.
Jahr: 2007
Contents
Preface xiii
I Boundary Value Problems and Iterative Methods 1
1 Finite Difference Approximations 3
1.1 Truncation errors............................. 5
1.2 Deriving finite difference approximations................ 7
1.3 Second order derivatives......................... 8
1.4 Higher order derivatives......................... 9
1.5 A general approach to deriving the coefficients............. 10
2 Steady States and Boundary Value Problems 13
2.1 The heat equation............................ 13
2.2 Boundary conditions........................... 14
2.3 The steady-state problem........................ 14
2.4 A simple finite difference method.................... 15
2.5 Local truncation error.......................... 17
2.6 Global error............................... 18
2.7 Stability................................. 18
2.8 Consistency............................... 19
2.9 Convergence............................... 19
2.10 Stability in the 2-norm.......................... 20
2.11 Green s functions and max-norm stability................ 22
2.12 Neumann boundary conditions..................... 29
2.13 Existence and uniqueness........................ 32
2.14 Ordering the unknowns and equations.................. 34
2.15 A general linear second order equation................. 35
2.16 Nonlinear equations........................... 37
2.16.1 Discretization of the nonlinear boundary value problem . 38
2.16.2 Nonuniqueness....................... 40
2.16.3 Accuracy on nonlinear equations............. 41
2.17 Singular perturbations and boundary layers............... 43
2.17.1 Interior layers....................... 46
vii
viii Contents
2.18 Nonuniform grids............................ 49
2.18.1 Adaptive mesh selection.................. 51
2.19 Continuation methods.......................... 52
2.20 Higher order methods.......................... 52
2.20.1 Fourth order differencing................. 52
2.20.2 Extrapolation methods................... 53
2.20.3 Deferred corrections.................... 54
2.21 Spectral methods............................. 55
3 Elliptic Equations 59
3.1 Steady-state heat conduction ...................... 59
3.2 The 5-point stencil for the Laplacian.................. 60
3.3 Ordering the unknowns and equations.................. 61
3.4 Accuracy and stability.......................... 63
3.5 The 9-point Laplacian.......................... 64
3.6 Other elliptic equations......................... 66
3.7 Solving the linear system........................ 66
3.7.1 Sparse storage in MATLAB................ 68
4 Iterative Methods for Sparse Linear Systems 69
4.1 Jacobi and Gauss-Seidel.........................69
4.2 Analysis of matrix splitting methods..................71
4.2.1 Rate of convergence....................74
4.2.2 Successive overtaxation.................76
4.3 Descent methods and conjugate gradients................78
4.3.1 The method of steepest descent..............79
4.3.2 The A-conjugate search direction............. 83
4.3.3 The conjugate-gradient algorithm............. 86
4.3.4 Convergence of conjugate gradient............ 88
4.3.5 Preconditioned ......................93
4.3.6 Incomplete Cholesky and ILU preconditioners......96
4.4 The Arnoldi process and GMRES algorithm..............96
4.4.1 Krylov methods based on three term recurrences.....99
4.4.2 Other applications of Arnoldi...............100
4.5 Newton-Krylov methods for nonlinear problems............101
4.6 Multigrid methods............................103
4.6.1 Slow convergence of Jacobi................103
4.6.2 The multigrid approach..................106
JI Initial Value Problems 111
5 The Initial Value Problem for Ordinary Differential Equations 113
5.1 Linear ordinary differential equations..................114
5.1.1 Duhamel s principle....................115
5.2 Lipschitz continuity...........................116
Contents ix
5.2.1 Existence and uniqueness of solutions........... 116
5.2.2 Systems of equations ................... 117
5.2.3 Significance of the Lipschitz constant........... 118
5.2.4 Limitations......................... 119
5.3 Some basic numerical methods..................... 120
5.4 Truncation errors............................. 121
5.5 One-step errors.............................. 122
5.6 Taylor series methods.......................... 123
5.7 Runge-Kutta methods.......................... 124
5.7.1 Embedded methods and error estimation......... 128
5.8 One-step versus multistep methods................... 130
5.9 Linear multistep methods........................ 131
5.9.1 Local truncation error................... 132
5.9.2 Characteristic polynomials................. 133
5.9.3 Starting values....................... 134
5.9.4 Predictor-corrector methods................ 135
6 Zero-Stability and Convergence for Initial Value Problems 137
6.1 Convergence...............................137
6.2 The test problem.............................138
6.3 One-step methods............................138
6.3.1 Euler s method on linear problems ............138
6.3.2 Relation to stability for boundary value problems.....140
6.3.3 Euler s method on nonlinear problems..........141
6.3.4 General one-step methods.................142
6.4 Zero-stability of linear multistep methods................143
6.4.1 Solving linear difference equations............144
7 Absolute Stability for Ordinary Differential Equations 149
7.1 Unstable computations with a zero-stable method...........149
7.2 Absolute stability............................151
7.3 Stability regions for linear multistep methods..............153
7.4 Systems of ordinary differential equations...............156
7.4.1 Chemical kinetics.....................157
7.4.2 Linear systems.......................158
7.4.3 Nonlinear systems.....................160
7.5 Practical choice of step size.......................161
7.6 Plotting stability regions.........................162
7.6.1 The boundary locus method for linear multistep methods . 162
7.6.2 Plotting stability regions of one-step methods.......163
7.7 Relative stability regions and order stars................164
8 Stiff Ordinary Differential Equations 167
8.1 Numerical difficulties..........................168
8.2 Characterizations of stiffness......................169
8.3 Numerical methods for stiff problems..................170
x Contents
8.3.1 A-stability and A(a)-stability...............171
8.3.2 L-stability.........................171
8.4 BDF methods..............................173
8.5 The TR-BDF2 method..........................175
8.6 Runge-Kutta-Chebyshev explicit methods...............175
9 Diffusion Equations and Parabolic Problems 181
9.1 Local truncation errors and order of accuracy.............. 183
9.2 Method of lines discretizations..................... 184
9.3 Stability theory.............................. 186
9.4 Stiffness of the heat equation...................... 186
9.5 Convergence............................... 189
9.5.1 PDE versus ODE stability theory............. 191
9.6 Von Neumann analysis ......................... 192
9.7 Multidimensional problems....................... 195
9.8 The locally one-dimensional method.................. 197
9.8.1 Boundary conditions.................... 198
9.8.2 The alternating direction implicit method......... 199
9.9 Other discretizations........................... 200
10 Advection Equations and Hyperbolic Systems 201
10.1 Advection................................201
10.2 Method of lines discretization......................203
10.2.1 Forward Euler time discretization.............204
10.2.2 Leapfrog..........................205
10.2.3 Lax-Friedrichs.......................206
10.3 The Lax-Wendroff method.......................207
10.3.1 Stability analysis......................209
10.4 Upwind methods.............................210
10.4.1 Stability analysis......................211
10.4.2 The Beam-Warming method ...............212
10.5 Von Neumann analysis .........................212
10.6 Characteristic tracing and interpolation.................214
10.7 The Courant-Friedrichs-Lewy condition................215
10.8 Some numerical results.........................218
10.9 Modified equations ...........................218
10.10 Hyperbolic systems...........................224
10.10.1 Characteristic variables..................224
10.11 Numerical methods for hyperbolic systems...............225
10.12 Initial boundary value problems.....................226
10.12.1 Analysis of upwind on the initial boundary value problem 226
10.12.2 Outflow boundary conditions...............228
10.13 Other discretizations...........................230
11 Mixed Equations 233
11.1 Some examples .............................233
Contents
11.2 Fully coupled method of lines......................235
11.3 Fully coupled Taylor series methods..................236
i 1.4 Fractional step methods.........................237
11.5 Implicit-explicit methods........................239
11.6 Exponential time differencing methods.................240
11.6.1 Implementing exponential time differencing methods . . 241
in Appendices 243
A Measuring Errors 245
A.I Errors in a scalar value..........................245
A.1.1 Absolute error.......................245
A.1.2 Relative error........................246
A.2 Big-oh and little-oh notation....................247
A.3 Errors in vectors.............................248
A.3.1 Norm equivalence.....................249
A.3.2 Matrix norms........................250
A.4 Errors in functions............................250
A.5 Errors in grid functions.........................251
A.5.1 Norm equivalence.....................252
A.6 Estimating errors in numerical solutions................254
A.6.1 Estimates from the true solution..............255
A.6.2 Estimates from a fine-grid solution............256
A.6.3 Estimates from coarser solutions.............256
B Polynomial Interpolation and Orthogonal Polynomials 259
B.I The general interpolation problem....................259
B.2 Polynomial interpolation ........................260
B.2.1 Monomial basis......................260
B.2.2 Lagrange basis.......................260
B.2.3 Newton form........................260
B.2.4 Error in polynomial interpolation.............262
B.3 Orthogonal polynomials.........................262
B.3.1 Legendre polynomials...................264
B.3.2 Chebyshev polynomials..................265
C Eigenvalues and Inner-Product Norms 269
C.I Similarity transformations........................270
C.2 Diagonalizable matrices.........................271
C.3 The Jordan canonical form .......................271
C.4 Symmetric and Hermitian matrices...................273
C.5 Skew-symmetric and skew-Hermitian matrices.............274
C.6 Normal matrices.............................274
C.7 Toeplitz and circulant matrices .....................275
C.8 The Gershgorin theorem.........................277
xii Contents
C.9 Inner-product norms...........................279
CIO Other inner-product norms .......................281
D Matrix Powers and Exponentials 285
D.I The resolvent ..............................286
D.2 Powers of matrices............................286
D.2.1 Solving linear difference equations............290
D.2.2 Resolvent estimates....................291
D.3 Matrix exponentials...........................293
D.3.1 Solving linear differential equations............296
D.4 Nonnormal matrices...........................296
D.4.1 Matrix powers.......................297
D.4.2 Matrix exponentials....................299
D.5 Pseudospectra..............................302
D.5.1 Nonnormality of a Jordan block..............304
D.6 Stable families of matrices and the Kreiss matrix theorem.......304
D.7 Variable coefficient problems......................307
E Partial Differential Equations 311
E.I Classification of differential equations.................311
E.I.I Second order equations..................311
E.1.2 Elliptic equations .....................312
E.I.3 Parabolic equations ....................313
E.I.4 Hyperbolic equations...................313
E.2 Derivation of partial differential equations from conservation principles 314
E.2.1 Advection.........................315
E.2.2 Diffusion..........................316
E.2.3 Source terms........................317
E.2.4 Reaction-diffusion equations ...............317
E.3 Fourier analysis of linear partial differential equations.........317
E.3.1 Fourier transforms.....................318
E.3.2 The advection equation..................318
E.3.3 The heat equation.....................320
E.3.4 The backward heat equation................322
E.3.5 More general parabolic equations.............322
E.3.6 Dispersive waves......................323
E.3.7 Even-versus odd-order derivatives............324
E.3.8 The Schrodinger equation.................324
E.3.9 The dispersion relation...................325
E.3.10 Wave packets........................327
Bibliography 329
Index 337
|
| adam_txt |
Titel: Finite difference methods for ordinary and partial differential equations
Autor: LeVeque, Randall J.
Jahr: 2007
Contents
Preface xiii
I Boundary Value Problems and Iterative Methods 1
1 Finite Difference Approximations 3
1.1 Truncation errors. 5
1.2 Deriving finite difference approximations. 7
1.3 Second order derivatives. 8
1.4 Higher order derivatives. 9
1.5 A general approach to deriving the coefficients. 10
2 Steady States and Boundary Value Problems 13
2.1 The heat equation. 13
2.2 Boundary conditions. 14
2.3 The steady-state problem. 14
2.4 A simple finite difference method. 15
2.5 Local truncation error. 17
2.6 Global error. 18
2.7 Stability. 18
2.8 Consistency. 19
2.9 Convergence. 19
2.10 Stability in the 2-norm. 20
2.11 Green's functions and max-norm stability. 22
2.12 Neumann boundary conditions. 29
2.13 Existence and uniqueness. 32
2.14 Ordering the unknowns and equations. 34
2.15 A general linear second order equation. 35
2.16 Nonlinear equations. 37
2.16.1 Discretization of the nonlinear boundary value problem . 38
2.16.2 Nonuniqueness. 40
2.16.3 Accuracy on nonlinear equations. 41
2.17 Singular perturbations and boundary layers. 43
2.17.1 Interior layers. 46
vii
viii Contents
2.18 Nonuniform grids. 49
2.18.1 Adaptive mesh selection. 51
2.19 Continuation methods. 52
2.20 Higher order methods. 52
2.20.1 Fourth order differencing. 52
2.20.2 Extrapolation methods. 53
2.20.3 Deferred corrections. 54
2.21 Spectral methods. 55
3 Elliptic Equations 59
3.1 Steady-state heat conduction . 59
3.2 The 5-point stencil for the Laplacian. 60
3.3 Ordering the unknowns and equations. 61
3.4 Accuracy and stability. 63
3.5 The 9-point Laplacian. 64
3.6 Other elliptic equations. 66
3.7 Solving the linear system. 66
3.7.1 Sparse storage in MATLAB. 68
4 Iterative Methods for Sparse Linear Systems 69
4.1 Jacobi and Gauss-Seidel.69
4.2 Analysis of matrix splitting methods.71
4.2.1 Rate of convergence.74
4.2.2 Successive overtaxation.76
4.3 Descent methods and conjugate gradients.78
4.3.1 The method of steepest descent.79
4.3.2 The A-conjugate search direction. 83
4.3.3 The conjugate-gradient algorithm. 86
4.3.4 Convergence of conjugate gradient. 88
4.3.5 Preconditioned .93
4.3.6 Incomplete Cholesky and ILU preconditioners.96
4.4 The Arnoldi process and GMRES algorithm.96
4.4.1 Krylov methods based on three term recurrences.99
4.4.2 Other applications of Arnoldi.100
4.5 Newton-Krylov methods for nonlinear problems.101
4.6 Multigrid methods.103
4.6.1 Slow convergence of Jacobi.103
4.6.2 The multigrid approach.106
JI Initial Value Problems 111
5 The Initial Value Problem for Ordinary Differential Equations 113
5.1 Linear ordinary differential equations.114
5.1.1 Duhamel's principle.115
5.2 Lipschitz continuity.116
Contents ix
5.2.1 Existence and uniqueness of solutions. 116
5.2.2 Systems of equations . 117
5.2.3 Significance of the Lipschitz constant. 118
5.2.4 Limitations. 119
5.3 Some basic numerical methods. 120
5.4 Truncation errors. 121
5.5 One-step errors. 122
5.6 Taylor series methods. 123
5.7 Runge-Kutta methods. 124
5.7.1 Embedded methods and error estimation. 128
5.8 One-step versus multistep methods. 130
5.9 Linear multistep methods. 131
5.9.1 Local truncation error. 132
5.9.2 Characteristic polynomials. 133
5.9.3 Starting values. 134
5.9.4 Predictor-corrector methods. 135
6 Zero-Stability and Convergence for Initial Value Problems 137
6.1 Convergence.137
6.2 The test problem.138
6.3 One-step methods.138
6.3.1 Euler's method on linear problems .138
6.3.2 Relation to stability for boundary value problems.140
6.3.3 Euler's method on nonlinear problems.141
6.3.4 General one-step methods.142
6.4 Zero-stability of linear multistep methods.143
6.4.1 Solving linear difference equations.144
7 Absolute Stability for Ordinary Differential Equations 149
7.1 Unstable computations with a zero-stable method.149
7.2 Absolute stability.151
7.3 Stability regions for linear multistep methods.153
7.4 Systems of ordinary differential equations.156
7.4.1 Chemical kinetics.157
7.4.2 Linear systems.158
7.4.3 Nonlinear systems.160
7.5 Practical choice of step size.161
7.6 Plotting stability regions.162
7.6.1 The boundary locus method for linear multistep methods . 162
7.6.2 Plotting stability regions of one-step methods.163
7.7 Relative stability regions and order stars.164
8 Stiff Ordinary Differential Equations 167
8.1 Numerical difficulties.168
8.2 Characterizations of stiffness.169
8.3 Numerical methods for stiff problems.170
x Contents
8.3.1 A-stability and A(a)-stability.171
8.3.2 L-stability.171
8.4 BDF methods.173
8.5 The TR-BDF2 method.175
8.6 Runge-Kutta-Chebyshev explicit methods.175
9 Diffusion Equations and Parabolic Problems 181
9.1 Local truncation errors and order of accuracy. 183
9.2 Method of lines discretizations. 184
9.3 Stability theory. 186
9.4 Stiffness of the heat equation. 186
9.5 Convergence. 189
9.5.1 PDE versus ODE stability theory. 191
9.6 Von Neumann analysis . 192
9.7 Multidimensional problems. 195
9.8 The locally one-dimensional method. 197
9.8.1 Boundary conditions. 198
9.8.2 The alternating direction implicit method. 199
9.9 Other discretizations. 200
10 Advection Equations and Hyperbolic Systems 201
10.1 Advection.201
10.2 Method of lines discretization.203
10.2.1 Forward Euler time discretization.204
10.2.2 Leapfrog.205
10.2.3 Lax-Friedrichs.206
10.3 The Lax-Wendroff method.207
10.3.1 Stability analysis.209
10.4 Upwind methods.210
10.4.1 Stability analysis.211
10.4.2 The Beam-Warming method .212
10.5 Von Neumann analysis .212
10.6 Characteristic tracing and interpolation.214
10.7 The Courant-Friedrichs-Lewy condition.215
10.8 Some numerical results.218
10.9 Modified equations .218
10.10 Hyperbolic systems.224
10.10.1 Characteristic variables.224
10.11 Numerical methods for hyperbolic systems.225
10.12 Initial boundary value problems.226
10.12.1 Analysis of upwind on the initial boundary value problem 226
10.12.2 Outflow boundary conditions.228
10.13 Other discretizations.230
11 Mixed Equations 233
11.1 Some examples .233
Contents
11.2 Fully coupled method of lines.235
11.3 Fully coupled Taylor series methods.236
i 1.4 Fractional step methods.237
11.5 Implicit-explicit methods.239
11.6 Exponential time differencing methods.240
11.6.1 Implementing exponential time differencing methods . . 241
in Appendices 243
A Measuring Errors 245
A.I Errors in a scalar value.245
A.1.1 Absolute error.245
A.1.2 Relative error.246
A.2 "Big-oh" and "little-oh" notation.247
A.3 Errors in vectors.248
A.3.1 Norm equivalence.249
A.3.2 Matrix norms.250
A.4 Errors in functions.250
A.5 Errors in grid functions.251
A.5.1 Norm equivalence.252
A.6 Estimating errors in numerical solutions.254
A.6.1 Estimates from the true solution.255
A.6.2 Estimates from a fine-grid solution.256
A.6.3 Estimates from coarser solutions.256
B Polynomial Interpolation and Orthogonal Polynomials 259
B.I The general interpolation problem.259
B.2 Polynomial interpolation .260
B.2.1 Monomial basis.260
B.2.2 Lagrange basis.260
B.2.3 Newton form.260
B.2.4 Error in polynomial interpolation.262
B.3 Orthogonal polynomials.262
B.3.1 Legendre polynomials.264
B.3.2 Chebyshev polynomials.265
C Eigenvalues and Inner-Product Norms 269
C.I Similarity transformations.270
C.2 Diagonalizable matrices.271
C.3 The Jordan canonical form .271
C.4 Symmetric and Hermitian matrices.273
C.5 Skew-symmetric and skew-Hermitian matrices.274
C.6 Normal matrices.274
C.7 Toeplitz and circulant matrices .275
C.8 The Gershgorin theorem.277
xii Contents
C.9 Inner-product norms.279
CIO Other inner-product norms .281
D Matrix Powers and Exponentials 285
D.I The resolvent .286
D.2 Powers of matrices.286
D.2.1 Solving linear difference equations.290
D.2.2 Resolvent estimates.291
D.3 Matrix exponentials.293
D.3.1 Solving linear differential equations.296
D.4 Nonnormal matrices.296
D.4.1 Matrix powers.297
D.4.2 Matrix exponentials.299
D.5 Pseudospectra.302
D.5.1 Nonnormality of a Jordan block.304
D.6 Stable families of matrices and the Kreiss matrix theorem.304
D.7 Variable coefficient problems.307
E Partial Differential Equations 311
E.I Classification of differential equations.311
E.I.I Second order equations.311
E.1.2 Elliptic equations .312
E.I.3 Parabolic equations .313
E.I.4 Hyperbolic equations.313
E.2 Derivation of partial differential equations from conservation principles 314
E.2.1 Advection.315
E.2.2 Diffusion.316
E.2.3 Source terms.317
E.2.4 Reaction-diffusion equations .317
E.3 Fourier analysis of linear partial differential equations.317
E.3.1 Fourier transforms.318
E.3.2 The advection equation.318
E.3.3 The heat equation.320
E.3.4 The backward heat equation.322
E.3.5 More general parabolic equations.322
E.3.6 Dispersive waves.323
E.3.7 Even-versus odd-order derivatives.324
E.3.8 The Schrodinger equation.324
E.3.9 The dispersion relation.325
E.3.10 Wave packets.327
Bibliography 329
Index 337 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | LeVeque, Randall J. 1955- |
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| id | DE-604.BV022492161 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:52:19Z |
| indexdate | 2024-07-09T20:58:47Z |
| institution | BVB |
| isbn | 9780898716290 |
| language | English |
| lccn | 2007061732 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015699357 |
| oclc_num | 86110147 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-92 DE-29T DE-91G DE-BY-TUM DE-634 DE-19 DE-BY-UBM |
| owner_facet | DE-20 DE-703 DE-92 DE-29T DE-91G DE-BY-TUM DE-634 DE-19 DE-BY-UBM |
| physical | XV, 341 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | Other titles in applied mathematics |
| series2 | Other titles in applied mathematics |
| spelling | LeVeque, Randall J. 1955- Verfasser (DE-588)112053688 aut Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems Randall J. LeVeque Philadelphia , PA Society for Industrial and Applied Mathematics 2007 XV, 341 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Other titles in applied mathematics 98 Includes bibliographical references and index Introductory textbook from which students can approach more advance topics relating to finite difference methods. Finite differences Differential equations Finite-Differenzen-Methode (DE-588)4194626-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differenzenverfahren (DE-588)4134362-1 gnd rswk-swf Differenzenverfahren (DE-588)4134362-1 s Differentialgleichung (DE-588)4012249-9 s DE-604 Finite-Differenzen-Methode (DE-588)4194626-1 s Other titles in applied mathematics 98 (DE-604)BV023088396 98 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015699357&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | LeVeque, Randall J. 1955- Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems Other titles in applied mathematics Finite differences Differential equations Finite-Differenzen-Methode (DE-588)4194626-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Differenzenverfahren (DE-588)4134362-1 gnd |
| subject_GND | (DE-588)4194626-1 (DE-588)4012249-9 (DE-588)4134362-1 |
| title | Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems |
| title_auth | Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems |
| title_exact_search | Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems |
| title_exact_search_txtP | Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems |
| title_full | Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems Randall J. LeVeque |
| title_fullStr | Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems Randall J. LeVeque |
| title_full_unstemmed | Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems Randall J. LeVeque |
| title_short | Finite difference methods for ordinary and partial differential equations |
| title_sort | finite difference methods for ordinary and partial differential equations steady state and time dependent problems |
| title_sub | steady-state and time-dependent problems |
| topic | Finite differences Differential equations Finite-Differenzen-Methode (DE-588)4194626-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Differenzenverfahren (DE-588)4134362-1 gnd |
| topic_facet | Finite differences Differential equations Finite-Differenzen-Methode Differentialgleichung Differenzenverfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015699357&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023088396 |
| work_keys_str_mv | AT levequerandallj finitedifferencemethodsforordinaryandpartialdifferentialequationssteadystateandtimedependentproblems |