An iterative reproducing kernel method in Hilbert space for the multi-point boundary value problems

In this paper, an iterative method is proposed to solve the nonlinear Bitsadze–Samarskii boundary value problems with multi-point boundary conditions. The algorithm is based on the reproducing kernel Hilbert space method. We use an iterative scheme to overcome the nonlinearity of the problem. The co...

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Vydané v:Journal of computational and applied mathematics Ročník 328; s. 151 - 163
Hlavní autori: Azarnavid, Babak, Parand, Kourosh
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 15.01.2018
Predmet:
Convergence
Error estimate
Iterative reproducing kernel Hilbert space method
Multi-point boundary conditions
Multi-point boundary conditions
Iterative reproducing kernel Hilbert space method
Error estimate
Convergence
ISSN:0377-0427, 1879-1778
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Popis
Shrnutí:In this paper, an iterative method is proposed to solve the nonlinear Bitsadze–Samarskii boundary value problems with multi-point boundary conditions. The algorithm is based on the reproducing kernel Hilbert space method. We use an iterative scheme to overcome the nonlinearity of the problem. The convergence and error estimate of the iterative scheme are established. The reproducing kernel Hilbert space method is used to generate an approximation of the linearized problem. In fact, the reproducing kernel Hilbert space method is combined with an iterative scheme to approximate the solution and an error estimate of the approximate solution is derived. In order to show the efficiency and versatility of the proposed method, some numerical results are reported. The comparison of numerical results with the analytical solution and the best results reported in the literature confirms the good accuracy and applicability of the proposed method.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2017.07.015