A fourth-order compact finite difference method for higher-order Lidstone boundary value problems

Authors:
Yuan-Ming Wang;Hai-Yun Jiang;Ravi P. Agarwal
Affiliations:
Department of Mathematics, East China Normal University, Shanghai 200241, People's Republic of China and Division of Computational Science, E-Institute of Shanghai Universities, Shanghai Normal Un ...;Department of Mathematics, East China Normal University, Shanghai 200241, People's Republic of China;Department of Mathematical Sciences, Florida Institute of Technology, 150 West University Boulevard, Melbourne, FL 32901, USA
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 2
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Abstract

A compact finite difference method is proposed for a general class of 2nth-order Lidstone boundary value problems. The existence and uniqueness of the finite difference solution is investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear term. A monotone iteration process is provided for solving the resulting discrete system efficiently, and a simple and easily verified condition is obtained to guarantee a geometric convergence of the iterations. The convergence of the finite difference solution and the fourth-order accuracy of the proposed method are proved. Numerical results demonstrate the high efficiency and advantages of this new approach.