A numerical solution to nonlinear multi-point boundary value problems in the reproducing kernel space. (English) Zbl 1206.65187

Lin, Yingzhen; Cui, Minggen

Math. Methods Appl. Sci. 34, No. 1, 44-47 (2011).

Summary: A new numerical algorithm is provided to solve nonlinear multi-point boundary value problems in a very favorable reproducing kernel space, which satisfies all complex boundary conditions. Its reproducing kernel function is discussed in detail. The theorem proves that the approximate solution and its first- and second-order derivatives all converge uniformly. The numerical experiments show that the algorithm is quite accurate and efficient for solving nonlinear multi-point boundary value problems.

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations
46E22	Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)

Keywords:

nonlinear problems; multi-point boundary value conditions; reproducing kernel space; convergence; algorithm; numerical experiments

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