A Sixth-Order Explicit Single-Step Nonlinear Numerical Method

Abstract

In this work, a sixth-order explicit single step non-linear method for solving initial value problems whose solutions possess singularities is constructed. The stability and convergence properties of the constructed method are investigated. Also, the associated local truncation error is presented. Using some standard test problems, the accuracy and efficiency of the method are established by its implementation and the results obtained are compared with those discussed in the literature.