Numerical-analytic Methods In Theory Of Boundary- Value Problems

By: Miklos Ronto, Anatoliy M. Samoilenko

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Hardcover | 3 July 2000

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468 Pages

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21.59 x 15.88 x 3.18

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This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods (NAM) for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory -- namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs.

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Preface
Introduction	p. 1
Numerical-Analytic Method of Successive Approximations for Two-Point Boundary-Value Problems	p. 19
Abstract Scheme of the Method	p. 19
Choice of the Form of Successive Approximations and Their Uniform Convergence	p. 26
Sufficient Conditions for the Existence of Solutions	p. 41
Necessary Conditions for the Solvability of the Boundary-Value Problem	p. 45
Error of Calculation of the Initial Value of a Solution	p. 52
Special Types of Successive Approximations and Estimates	p. 64
Numerical-Analytic Method in the Case of Nonlinear Two-Point Boundary Conditions	p. 72
Boundary-Value Problems with Small Parameter	p. 81
Modification of the Numerical-Analytic Method for Two-Point Boundary-Value Problems	p. 89
Periodic Boundary-Value Problem	p. 89
Theorems on the Properties of Determining Functions of a Periodic Boundary-Value Problem	p. 98
Solvability of the Approximate Determining Equation and the Error of the Initial Value of a Periodic Solution	p. 105
Modification of the Method for Two-Point Problems	p. 115
Relationship between Exact and Approximate Determining Equations	p. 123
Determination of Initial Values of Solutions of Two-Point Boundary-Value Problems	p. 131
Realization of the Method for Systems of Two Equations	p. 142
Numerical-Analytic Method for Boundary-Value Problems with Parameters in Boundary Conditions	p. 149
Successive Approximations for Problems with One Parameter in Linear Boundary Conditions	p. 150
Sufficient Solvability Conditions and Determination of the Initial Value of a Solution of the Boundary-Value Problem with Parameter	p. 158
Boundary-Value Problems with Nonfixed Right Boundary	p. 168
Solvability Theorems for Problems with Nonfixed Right Boundary	p. 177
The Case of Several Parameters in Boundary Conditions	p. 193
Linear Dependence of Boundary Conditions on Two Parameters	p. 209
Collocation Method for Boundary-Value Problems with Impulses	p. 221
Green Function of a Homogeneous Two-Point Boundary-Value Problem	p. 222
Inhomogeneous Linear Impulsive Boundary-Value Problems	p. 229
Convergence of the Algebraic Collocation Method of Nonlinear Systems	p. 234
Method of Trigonometric Collocation for Periodic Systems	p. 245
Practical Solution of Impulsive Problems	p. 250
Green Function for a Three-Point Boundary-Value Problem with Single Impulse Influence	p. 257
Semihomogeneous Linear Two-Point Boundary-Value Problem with m-Impulse Influence	p. 271
Inhomogeneous Linear m-Impulse Two-Point Boundary-Value Problem	p. 279
Multipoint m-Impulse Boundary-Value Problem	p. 280
Equations with Piecewise-Continuous Right-Hand Side	p. 286
Construction of Solutions of Two-Impulse Systems	p. 308
The Theory of the Numerical-Analytic Method: Achievements and New Trends of Development	p. 317
References	p. 415
Table of Contents provided by Blackwell. All Rights Reserved.

Numerical-analytic Methods In Theory Of Boundary- Value Problems

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Hardcover

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