A fourth-order compact finite difference method for higher-order Lidstone boundary value problems ?
A compact finite difference method is proposed for a general class of 2n 2 n th-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.
compact finite difference method monotone iterations fourth-order accuracy 2n 2 n th-order lidstone boundary value problem 2n 2 n 2n 2 n 2 n rate of convergence