Optimized Three-step Hybrid Block Method for Stiff Problems in Ordinary Differential Equations

This paper presents the construction and implementation of a three-step optimized hybrid method for solving stiff system of first order initial value problems of ordinary differential equations. The method contains six implicit formulas which were obtained from a continuous approximation, using shifted chebyshev polynomial as the basis function, via evaluations at six different points on the selected three-step including three optimized intra-step points. The method is consistent, zero-stable and convergent. Numerical experiments are included to show the competitive and superior strength of the proposed method for solving these kinds of problems over similar properties of methods in literature.