A variable step-size implementation of a new one-step block method for integrating Burgers' model equation

Abstract

This article proposes a variable stepsize implementation of an improved one-step block method (OBM) that uses two intermediate points to solve Burgers' equation. The model's problems under consideration are semi-discretized by reducing them into an equivalent differential system using the method of lines. The OBM is improved with an embedding-like method executed in variable stepsize mode. A few of Burgers' real-life model problems are numerically solved to test the accuracy of our error estimation and mesh selection strategy. The numerical results confirmed that the variable stepsize implementation used in this manuscript performed better than the fixed stepsize implementation.