A fourth-order compact finite difference method for nonlinear higher-order multi-point boundary value problems

作者：Wang, Yuan-Ming^*; Wu, Wen-Jia; Agarwal, Ravi P.

来源：Computers & Mathematics with Applications, 2011, 61(11): 3226-3245.

DOI：10.1016/j.camwa.2011.04.016

• 2nth-order multi-point boundary value problem
• Compact finite difference method
• Fourth-order accuracy
• Monotone iterations
• Upper and lower solutions

A fourth-order compact finite difference method is proposed for a class of nonlinear 2nth-order multi-point boundary value problems. The multi-point boundary condition under consideration includes various commonly discussed boundary conditions, such as the three- or four-point boundary condition, (n + 2)-point boundary condition and 2(n - m)-point boundary condition. The existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear term. The convergence and the fourth-order accuracy of the method are proved. An efficient monotone iterative algorithm is developed for solving the resulting nonlinear finite difference systems. Various sufficient conditions for the construction of upper and lower solutions are obtained. Some applications and numerical results are given to demonstrate the high efficiency and advantages of this new approach.

• 出版日期2011-6
• 单位上海大学; 华东师范大学; 中国石油大学（北京）; 上海师范大学