Nested Second Derivative General Linear Methods

Abstract

A family of nested second derivative general linear methods (NSDGLMs) which combines the advantages of linear multistep methods and Runge – Kutta methods is presented. The method possess high order with A-stability property, making it suitable for solving stiff initial value problems of ordinary differential equation. In implementation, the NSDGLM avoids the disadvantages of poor stability of linear multistep methods and high cost of implementation of Runge -Kutta methods. Numerical experiment was carried out on the Van der Pol equation, and it is observed that the numerical results of the NSDGLM compares with the reference solution from the MATLAB ode15s