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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.
MSC:
65L10Boundary value problems for ODE (numerical methods)
34B05Linear boundary value problems for ODE
46E22Hilbert spaces with reproducing kernels
References:
[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