Numerical-analytic methods in the theory of boundary-value problems /
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| Author / Creator: | Ronto, N. I. (Nikolaĭ Iosifovich) |
|---|---|
| Imprint: | Singapore ; River Edge, NJ : World Scientific, c2000. |
| Description: | ix, 455 p : ill. ; 23 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4326619 |
Table of Contents:
- Ch. 1. Numerical-Analytic Method of Successive Approximations for Two-Point Boundary-Value Problems. 1. Abstract Scheme of the Method. 2. Choice of the Form of Successive Approximations and Their Uniform Convergence. 3. Sufficient Conditions for the Existence of Solutions. 4. Necessary Conditions for the Solvability of the Boundary-Value Problem. 5. Error of Calculation of the Initial Value of a Solution. 6. Special Types of Successive Approximations and Estimates. 7. Numerical-Analytic Method in the Case of Nonlinear Two-Point Boundary Conditions. 8. Boundary-Value Problems with Small Parameter
- Ch. 2. Modification of the Numerical-Analytic Method for Two-Point Boundary-Value Problems. 9. Periodic Boundary-Value Problem. 10. Theorems on the Properties of Determining Functions of a Periodic Boundary-Value Problem. 11. Solvability of the Approximate Determining Equation and the Error of the Initial Value of a Periodic Solution. 12. Modification of the Method for Two-Point Problems. 13. Relationship between Exact and Approximate Determining Equations. 14. Determination of Initial Values of Solutions of Two-Point Boundary-Value Problems. 15. Realization of the Method for Systems of Two Equations
- Ch. 3. Numerical-Analytic Method for Boundary-Value Problems with Parameters in Boundary Conditions. 16. Successive Approximations for Problems with One Parameter in Linear Boundary Conditions. 17. Sufficient Solvability Conditions and Determination of the Initial Value of a Solution of the Boundary-Value Problem with Parameter. 18. Boundary-Value Problems with Nonfixed Right Boundary. 19. Solvability Theorems for Problems with Nonfixed Right Boundary. 20. The Case of Several Parameters in Boundary Conditions. 21. Linear Dependence of Boundary Conditions on Two Parameters
- Ch. 4. Collocation Method for Boundary-Value Problems with Impulses. 22. Green Function of a Homogeneous Two-Point Boundary-Value Problem. 23. Inhomogeneous Linear Impulsive Boundary-Value Problems. 24. Convergence of the Algebraic Collocation Method of Nonlinear Systems. 25. Method of Trigonometric Collocation for Periodic Systems. 26. Practical Solution of Impulsive Problems. 27. Green Function for a Three-Point Boundary-Value Problem with Single Impulse Influence. 28. Semihomogeneous Linear Two-Point Boundary-Value Problem with m-Impulse Influence. 29. Inhomogeneous Linear m-Impulse Two-Point Boundary-Value Problem. 30. Multipoint m-Impulse Boundary-Value Problem. 31. Equations with Piecewise-Continuous Right-Hand Side. 32. Construction of Solutions of Two-Impulse Systems. App. The Theory of the Numerical-Analytic Method: Achievements and New Trends of Development.
