A new adaptive nonlinear numerical method for singular and stiff differential problems

Abstract

In this work, a new adaptive numerical method is proposed for solving nonlinear, singular, and stiff initial value problems often encountered in real life. Starting with a fixed step size, the new method’s performance can be significantly enhanced by introducing an adaptive step-size approach. The qualitative properties of the proposed method have been investigated to determine the efficiency and reliability of the method. The proposed method is of fifth-order accuracy, zero stable, L-stable, and consistent. In addition, the proposed method is convergent, and its stability properties are also shown through its Order Stars. Finally, numerical experiments are conducted to illustrate the performance of the method. The results obtained show that the proposed method compares favourably with existing methods.