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Lin, Yingzhen; Niu, Jing; Cui, Minggen

A numerical solution to nonlinear second order three-point boundary value problems in the reproducing kernel space. (English) Zbl 1246.65122

Appl. Math. Comput. 218, No. 14, 7362-7368 (2012).
Summary: A new numerical algorithm is provided to solve nonlinear three-point boundary value problems in a very favorable reproducing kernel space which satisfies all boundary conditions. Its reproducing kernel function is discussed in detail. We also prove 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 second order three-point boundary value problems.

Cited in 21 Documents

MSC:

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

Keywords:

algorithm; reproducing kernel function; nonlinear three-point boundary value problems; numerical experiments
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\textit{Y. Lin} et al., Appl. Math. Comput. 218, No. 14, 7362--7368 (2012; Zbl 1246.65122)
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