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A new method for solving a class of mixed boundary value problems with singular coefficient. (English) Zbl 1202.65095
Summary: We give a new method to deal with boundary value conditions. The main contribution of this paper is to put mixed boundary value conditions into a reproducing kernel Hilbert space. Numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.
65L10Boundary value problems for ODE (numerical methods)
34B05Linear boundary value problems for ODE
46E22Hilbert spaces with reproducing kernels
[1]Yulan, Wang; Lu, Chao: Using reproducing kernel for solving a class of partial differential equation with variable-coefficients, Applied mathematics and mechanics 29, 129-137 (2008) · Zbl 1231.41019 · doi:10.1007/s10483-008-0115-y
[2]Wang, Yulan; Chaolu, Temuer; Chen, Zhong: Using reproducing kernel for solving a class of singular weakly nonlinear boundary value problems, International journal of computer mathematics 87, 367-380 (2010) · Zbl 1185.65134 · doi:10.1080/00207160802047640
[3]Du, Hong; Cui, Minggen: Approximate solution of the Fredholm integral equation of the first kind in a reproducing kernel Hilbert space, Applied mathematics letters 21, 617-623 (2008) · Zbl 1145.65113 · doi:10.1016/j.aml.2007.07.014
[4]Yao, Huanmin; Cui, Minggen: A new algorithm for a class of singular boundary value problems, Applied mathematics and computation 186, 1183-1191 (2007) · Zbl 1175.65085 · doi:10.1016/j.amc.2006.07.157
[5]Yulan, Wang; Chaolu, Temuer; Jing, Pang: New algorithm for second-order boundary value problems of integro-differential equation, Journal of computational and applied mathematics 229, 1-6 (2009) · Zbl 1180.65180 · doi:10.1016/j.cam.2008.10.007
[6]Lü, Xueqin; Cui, Minggen: Analytic solutions to a class of nonlinear infinite-delay-differential equations, Journal of mathematical analysis and applications 343, 724-732 (2008) · Zbl 1160.34059 · doi:10.1016/j.jmaa.2008.01.101
[7]Geng, Fazhan; Cui, Minggen: Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space, Applied mathematics and computation 192, 389-398 (2007) · Zbl 1193.34017 · doi:10.1016/j.amc.2007.03.016