A new family of <i>L</i>-stable block methods with relative measure of stability

Abstract

There are several nonlinear and stiff mathematical models in fields of science and engineering that have always remained a challenge for numerical analysts and applied mathematicians. Various numerical methods are proposed to deal with stiff models; however, it requires the model to have strong stability characteristics to handle the stiffness in the model. This paper develops a new family of L-stable block methods with a relative measure of stability for the solution of stiff differential equations with different characteristics. First, the theoretical properties of the proposed block method in terms of local truncation errors, absolute stability, consistency, convergence, and order stars have been analysed and investigated. Then, seven illustrative stiff differential models have been solved to measure the proposed method's performance, suitability, effectiveness, and efficiency. Finally, the error distributions and the precision factors are computed in the comparison of several existing methods having similar properties as that of the proposed L-stable block method.