Screen LibraryNumerical-analytic methods in the theory of boundary-value problems /
This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory...
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| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore : |
| Publication Dates: | 2000. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/3962#t=toc |
| Summary: |
This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods 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. The Appendix, written in collaboration with S. I. Trofimchuk, discusses the connection of the new method with the classical Cesari, Cesari-Hale and Lyapunov-Schmidt methods. |
| Carrier Form: | 1 online resource (ix,455pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 415-455) |
| ISBN: | 9789812813602 |
| CLC: | O175.8 |
| 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 for 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. |