Derivation of a Six-Step Block Method for Direct Solution of Second Order Ordinary Differential Equations

[摘要] A new six-step block method for solving second order initial value problems of ordinary differential equations is proposed using interpolation and collocation strategies. In developing this method, the power series adopted as an approximate solution is employed as interpolation equation while its second derivative is used as collocation equation. In addition, the stability properties of the developed method are also established. The numerical results reveal that the new method produces better accuracy if compared to existing methods when solving the same problems.

[学科分类] 计算数学

[关键词] power series;interpolation;collocation;block  method;ordinary differential equations