New A-stable scheme for initial value problems of ODEs

This paper proposes the construction of a new explicit scheme for the numerical solution of initial value problems of ordinary differential equations(ODEs). The scheme is constructed by considering a suitable approximation to the theoretical solution, which has the second order convergence and is A-stable. The proposed scheme has been tested on a variety of initial value problems. Further, it can also be used to solve a system of first order ODEs. Numerical examples are given to illustrate the efficiency and performance of the proposed scheme in comparison with the classical two-step Adams-Bashforth method and the second order Taylor series method.