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A numerical solution to nonlinear second order three-point boundary value problems in the reproducing kernel space. (English) Zbl 1246.65122
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.
MSC:
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
46E22Hilbert spaces with reproducing kernels
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