New Parallel R-point explicit block method for solving linear high-order ordinary differential equations directly

Abstract

A new method called parallel R-point explicit block method for solving a single equation of higher order ordinary differential equation directly using a constant step size is developed. This method calculates the numerical solution at R point simultaneously and is parallel in nature. Computational advantages are presented by comparing the results obtained with the new method with that of the conventional 1-point method. The numerical results show that the new method reduces the total number of steps and execution time. The accuracy of the parallel block and the conventional 1-point method is comparable particularly when finer step sizes are used.