Solving ordinary and partial boundary value problems in science and engineering:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
1999
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| Series: | CRC series in computational mechanics and applied analysis
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 202 S. graph. Darst. |
| ISBN: | 0849325528 |
Staff View
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| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
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Record in the Search Index
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| adam_text | SOLVING ORDINARY I PARTIM BOUNDARY VALUE PROBLE IN SCIENCE AND
ENGINEERING KAREL REKTORYS CRC PRESS BOCA RATON LONDON NEW YORK
WASHINGTON, D.C. CONTENTS INTRODUCTION 1 1 ORDINARY DIFFERENTIAL
EQUATIONS WITH BOUNDARY CONDITIONS; EIGEN- VALUE PROBLEMS 5 1.1
TECHNICAL MOTIVATION 5 1.2 RELATION BETWEEN THE PROBLEM (1.1.3) AND
(1.1.4) AND THE PROBLEM CORRESPONDING TO THE ZERO VERTICAL LOADING OF
THE BAR 10 1.3 BRIEF SUMMARY OF THE SPACE L,2(A,B) 11 1.4 EIGENVALUE
PROBLEMS 18 1.5 BASIC PROPERTIES OF EIGENVALUES AND EIGENFUNCTIONS 20
1.6 NONHOMOGENEOUS EQUATIONS WITH BOUNDARY CONDITIONS 27 1.7 THE
FINITE-DIFFERENCE METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS 37 1.8
CONVERGENCE OF THE FINITE-DIFFERENCE METHOD 40 1.9 APPLICATION OF THE
FINITE-DIFFERENCE METHOD IN EIGENVALUE PROBLEMS 41 1.10 PROBLEMS 1.10.1
TO 1.10.15 43 2 PARTIAL DIFFERENTIAL EQUATIONS: CLASSICAL APPROACH 55
2.1 BASIC CONCEPTS; EXAMPLES OF EQUATIONS FREQUENTLY ENCOUNTERED IN
APPLICATIONS; THE HEAT-CONDUCTION EQUATION DERIVED .... 55 2.2 BOUNDARY
VALUE PROBLEMS (EQUATIONS WITH BOUNDARY CONDITIONS); THE DIRICHLET
PROBLEM FOR LAPLACE AND POISSON EQUATIONS; THE MAXIMUM PRINCIPLE FOR
HARMONIE FUNCTIONS AND ITS CONSEQUENCES 62 2.3 THE HEAT-CONDUCTION
EQUATION 71 2.4 PROBLEMS 2.4.1 TO 2.4.12 77 X CONTENTS 3 VARIATIONAL
METHODS OF SOLUTION OF EUIPTICAL BOUNDARY VALUE PROB- LEMS; GENERALIZED
SOLUTIONS AND THEIR APPROXIMATIONS; WEAK SOLU- TIONS 85 3.1 THE EQUATION
AU = / 85 3.2 COMPARISON FUNCTIONS, DOMAIN OF DEFINITION OF OPERATOR A;
SYMMETRICAL, POSITIVE, AND POSITIVE-DEFINITE OPERATORS 90 3.3 THEOREM ON
MINIMUM OF FUNCTIONAL OF ENERGY 104 3.4 GENERALIZED DERIVATIVES; THE
ENERGETIC SPACE, THE SOBOLEV SPACE; GENERALIZED SOLUTIONS, WEAK
SOLUTIONS 111 3.4.1 FUNCTIONS OF ONE VARIABLE 111 3.4.2 FUNCTIONS OF
SEVERAL VARIABLES 122 3.5 THE RITZ AND GALERKIN METHODS; THE
FINITE-ELEMENT METHOD . . 122 3.6 EIGENVALUE PROBLEMS FOR EQUATIONS OF
ORDER 2K 137 3.7 PROBLEMS 3.7.1 TO 3.7.16 141 4 THE FINITE-DIFFERENCE
METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS; THE METHOD OF DISCRETIZATION
IN TIME (THE ROTHE METHOD) 155 4.1 THE FINITE-DIFFERENCE METHOD (THE
METHOD OF FINITE DIFFERENCES, THE NET METHOD) FOR PARTIAL DIFFERENTIAL
EQUATIONS 155 4.2 THE FINITE-DIFFERENCE METHOD FOR THE HEAT EQUATION 160
4.2.1 THE EXPLICIT SCHEME 160 4.2.2 THE IMPLICIT SCHEME 163 4.3 THE
METHOD OF DISCRETIZATION IN TIME (THE ROTHE METHOD, THE METHOD OF LINES)
166 4.4 PROBLEMS 4.4.1 TO 4.4.9 171 5 THE FOURIER METHOD 183 5.1 THE
FOURIER METHOD FOR ONE-DIMENSIONAL VIBRATION PROBLEMS . 183 5.2 PROBLEMS
5.2.1 TO 5.2.8 188 REFERENCES 197 INDEX 199
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| indexdate | 2024-07-09T18:30:36Z |
| institution | BVB |
| isbn | 0849325528 |
| language | English |
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| physical | X, 202 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | CRC Press |
| record_format | marc |
| series2 | CRC series in computational mechanics and applied analysis |
| spelling | Rektorys, Karel Verfasser aut Solving ordinary and partial boundary value problems in science and engineering Karel Rektorys Boca Raton [u.a.] CRC Press 1999 X, 202 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CRC series in computational mechanics and applied analysis Mathematik Naturwissenschaft Boundary value problems Numerical solutions Differential equations Numerical solutions Differential equations, Partial Numerical solutions Engineering mathematics Science Mathematics Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s Ingenieurwissenschaften (DE-588)4137304-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008566711&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rektorys, Karel Solving ordinary and partial boundary value problems in science and engineering Mathematik Naturwissenschaft Boundary value problems Numerical solutions Differential equations Numerical solutions Differential equations, Partial Numerical solutions Engineering mathematics Science Mathematics Ingenieurwissenschaften (DE-588)4137304-2 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4137304-2 (DE-588)4048395-2 |
| title | Solving ordinary and partial boundary value problems in science and engineering |
| title_auth | Solving ordinary and partial boundary value problems in science and engineering |
| title_exact_search | Solving ordinary and partial boundary value problems in science and engineering |
| title_full | Solving ordinary and partial boundary value problems in science and engineering Karel Rektorys |
| title_fullStr | Solving ordinary and partial boundary value problems in science and engineering Karel Rektorys |
| title_full_unstemmed | Solving ordinary and partial boundary value problems in science and engineering Karel Rektorys |
| title_short | Solving ordinary and partial boundary value problems in science and engineering |
| title_sort | solving ordinary and partial boundary value problems in science and engineering |
| topic | Mathematik Naturwissenschaft Boundary value problems Numerical solutions Differential equations Numerical solutions Differential equations, Partial Numerical solutions Engineering mathematics Science Mathematics Ingenieurwissenschaften (DE-588)4137304-2 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Mathematik Naturwissenschaft Boundary value problems Numerical solutions Differential equations Numerical solutions Differential equations, Partial Numerical solutions Engineering mathematics Science Mathematics Ingenieurwissenschaften Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008566711&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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