A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations

Abstract

We derive a variable step of the implicit block methods based on the backward differentiation formulae (BDF) for solving stiff initial value problems (IVPs). A simplified strategy in controlling the step size is proposed with the aim of optimizing the performance in terms of precision and computation time. The numerical results obtained support the enhancement of the method proposed as compared to MATLAB′s suite of ordinary differential equations (ODEs) solvers, namely, ode15s and ode23s.