Approximation methods for solutions of differential and integral equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht
VSP
1995
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 325 S. |
| ISBN: | 9067641944 |
Staff View
MARC
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| 100 | 1 | |a Dzjadyk, Vladislav Kirillovič |d 1919-1998 |e Verfasser |0 (DE-588)173116930 |4 aut | |
| 245 | 1 | 0 | |a Approximation methods for solutions of differential and integral equations |c V. K. Dzyadyk |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Utrecht |b VSP |c 1995 | |
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Record in the Search Index
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| adam_text | Contents
Preface 5
1 Introduction to approximation theory 9
1.1 Chebyshev theory of approximation of real functions 9
1.1.1 Existence theorem 9
1.1.2 Chebyshev theorem on the characterization of a polynomial
of best uniform approximation 11
1.1.3 Uniqueness theorem 17
1.1.4 Lower estimate of the value of best approximation 17
1.1.5 Chebyshev polynomials 19
1.1.6 Chebyshev polynomials of the second kind 23
1.1.7 An efficient construction of polynomials least
deviating from zero with polynomial weights 24
1.1.8 The notion of snakes 31
1.1.9 Chebyshev approximation of functions by rational polynomials 33
1.2 Linear methods of Fourier series summation and approximation of
continuous functions 37
1.2.1 Linear methods of Fourier series summation 38
1.2.2 Discrete polynomial linear operators 43
1.3 Lagrange interpolation polynomials 44
1.3.1 Fundamental Lagrange polynomials of a general form. Lebes
gue functions and constants 44
1.3.2 Periodic Lagrange polynomials constructed with
equidistant nodes and corresponding algebraic
Lagrange polynomials 47
1.3.3 Explicit formulas for Lebesgue constants in
interpolation constructed with optimal nodes 53
1.3.4 The representation of Lebesgue constants as sums of asymp¬
totic series 63
1.4 Estimating the best approximation of analytic functions on a segment
by polynomials 71
1
2
1.4.1 Basic definitions 71
1.4.2 Bernstein theorem 72
1.5 Estimates for the norms of trigonometric and algebraic polynomials
by their values at a discrete system of points 76
2 A simple approach to Fredholm integral equations of the second
kind and application of linear methods for approximating their so¬
lutions 81
2.1 Some preliminaries 81
2.2 Degenerate kernels 83
2.3 Basic theorem 86
2.4 Fredholm theorems 90
2.5 Theorems on resolvents 94
2.6 Methods for approximating the solutions of Fredholm integral equa¬
tions of the second kind 97
3 Iteration method for approximately solving differential and integral
equations 119
3.1 Picard s method for the Cauchy problem with an analytic right hand
side 119
3.2 Al method for approximating solutions of the Cauchy problem for
ordinary differential equations by polynomials 123
3.3 Al method for approximating solutions of certain nonlinear integral
equations by polynomials 132
4 Approximation method for solving ordinary linear differential equa¬
tions 145
4.1 Auxiliary facts 145
4.2 Methods that result from using a sequence of linear operators to solve
approximately differential equations 148
4.3 o method for approximating solutions of linear differential equations
with polynomial coefficients by polynomials 154
4.4 A posteriori estimates of errors for polynomial approximation of ODE
solutions 171
4.4.1 Nonlinear case 171
4.4.2 Linear case 173
4.5 o method for approximating the solution of boundary value problems
for OLDEPC and its derivatives by polynomials 174
4.6 Comparison of the a rnethod with Galerkin s method, Lanczos r
method and the Al method 188
Contents 3
5 Approximation of solutions of partial differential equations 193
5.1 Dirichlet problem for LDEPC of elliptic type in a rectangle 193
5.2 Approximate solution of the initial problem for LDEPC of parabolic
type in a semistrip 196
5.3 Application of the a method to LDEPC of hyperbolic type 197
5.3.1 The Goursat problem 197
5.3.2 The Cauchy problem 202
5.3.3 The mixed problem 206
5.4 The Al method for solving nonlinear Cauchy, Darboux and Goursat
problems for differential equations of hyperbolic type 209
6 Theory of transcendental functions and their approximation 225
6.1 Preliminaries 225
6.2 Formulas for the coefficients of the Newton polynomials and for the
derivatives of f(x)[g(x)]k 228
6.3 Investigation of Wronskian and its minors for a fundamental system
of solutions of LDE with a single regular singular point 234
6.4 Investigation of the Cauchy Green function for LDE with SRSP ... 237
6.5 Equations for analytic parts of special functions 246
6.6 Initial conditions for analytic solutions of LDE with SRSP 253
6.7 Efficient construction of polynomials for a close to the best approxi¬
mation of analytic parts of solutions of LDE with SRSP 255
7 Application of the a—method to the rational approximation and
integral representation of functions 267
7.1 Application of the a method to the rational approximation of solu¬
tions of Cauchy problems and Pade s approximation of elementary
functions 267
7.2 Construction of generalized moment representations 275
7.3 Application of generalized moment representations to Pade s approx¬
imation 280
7.4 Application of GMR to Pade s approximation of basic hypergeometric
series 286
7.5 Generalized moment representations and integral representations of
functions 292
7.6 Rational approximation of elementary functions on an interval .... 295
Bibliography 313
|
| any_adam_object | 1 |
| author | Dzjadyk, Vladislav Kirillovič 1919-1998 |
| author_GND | (DE-588)173116930 |
| author_facet | Dzjadyk, Vladislav Kirillovič 1919-1998 |
| author_role | aut |
| author_sort | Dzjadyk, Vladislav Kirillovič 1919-1998 |
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| building | Verbundindex |
| bvnumber | BV010699482 |
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| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010699482 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:57:24Z |
| institution | BVB |
| isbn | 9067641944 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007141330 |
| oclc_num | 260195437 |
| open_access_boolean | |
| owner | DE-12 DE-706 DE-83 |
| owner_facet | DE-12 DE-706 DE-83 |
| physical | 325 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | VSP |
| record_format | marc |
| spelling | Dzjadyk, Vladislav Kirillovič 1919-1998 Verfasser (DE-588)173116930 aut Approximation methods for solutions of differential and integral equations V. K. Dzyadyk 1. publ. Utrecht VSP 1995 325 S. txt rdacontent n rdamedia nc rdacarrier Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Approximation (DE-588)4002498-2 s DE-604 Integralgleichung (DE-588)4027229-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007141330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dzjadyk, Vladislav Kirillovič 1919-1998 Approximation methods for solutions of differential and integral equations Differentialgleichung (DE-588)4012249-9 gnd Integralgleichung (DE-588)4027229-1 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4027229-1 (DE-588)4002498-2 |
| title | Approximation methods for solutions of differential and integral equations |
| title_auth | Approximation methods for solutions of differential and integral equations |
| title_exact_search | Approximation methods for solutions of differential and integral equations |
| title_full | Approximation methods for solutions of differential and integral equations V. K. Dzyadyk |
| title_fullStr | Approximation methods for solutions of differential and integral equations V. K. Dzyadyk |
| title_full_unstemmed | Approximation methods for solutions of differential and integral equations V. K. Dzyadyk |
| title_short | Approximation methods for solutions of differential and integral equations |
| title_sort | approximation methods for solutions of differential and integral equations |
| topic | Differentialgleichung (DE-588)4012249-9 gnd Integralgleichung (DE-588)4027229-1 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Differentialgleichung Integralgleichung Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007141330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dzjadykvladislavkirillovic approximationmethodsforsolutionsofdifferentialandintegralequations |