L-stable Explicit Nonlinear Method with Constant and Variable Step-size Formulation for Solving Initial Value Problems

摘要

In this work, we develop a nonlinear explicit method suitable for both autonomous and non-autonomous type of initial value problems in Ordinary Differential Equations (ODEs). The method is found to be third order accurate having L-stability. It is shown that if a variable step-size strategy is employed then the performance of the proposed method is further improved in comparison with other methods of same nature and order. The method is shown to be working well for initial value problems having singular solutions, singularly perturbed and stiff problems, and blow-up ODE problems, which is illustrated using a few numerical experiments.