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

作者：Wang Yuan Ming; Jiang Hai Yun; Agarwal Ravi P^*

来源：Computers & Mathematics with Applications, 2008, 56(2): 499-521.

DOI：10.1016/j.camwa.2007.04.051

• 2nth-order Lidstone boundary value problem
• compact finite difference method
• fourth-order accuracy
• monotone iterations
• rate of convergence

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.

• 出版日期2008-7
• 单位上海大学; 华东师范大学