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

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.

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