A class of explicit two-step superstable methods for second-order linear initial value problems

Abstract

A class of explicit two-step superstable methods of fourth algebraic order for the numerical solution of second-order linear initial value problems is presented in this article. We need Taylor expansion at an internal grid point and collocation formulae for the derivatives of the solution to derive a method and then modify it into a class of methods having the desired stability properties. Computational results are presented to demonstrate the applicability of the methods to some standard problems.

Keywords:

• second-order linear initial value problems
• region of absolute stability
• interval of weak stability
• interval of periodicity
• superstability

2000 AMS Subject Classification: :

• 65L05
• 65L06