A family of matrix coefficient formulas for solving ordinary differential equations

A matrix form of coefficients is applied to develop a new family of one-step explicit methods. Clearly, this type of methods is different from the conventional methods that have scalar constant coefficients. This novel family of methods is governed by a free parameter and is characterized by problem dependency, where the initial physical properties to define the problem under analysis are applied to form the coefficients of the difference formula. In general, it can simultaneously combine A-stability, second order accuracy and explicit implementation. As a result, it is best suited to solve systems of nonlinear first order stiff ordinary differential equations since it is of high computational efficiency in contrast to conventional implicit methods.(c) 2021 Published by Elsevier Inc.