Solving Ordinary Differential Equation Using Parallel Seventh Order Runge-Kutta Method with Two Processors

This paper presents a derivation of the seventh order Runge-Kutta method with eight stages suitable for parallel implementation. The development of a parallel model is based on the second type of Runge-Kutta sparsity structure which is divided into two processors by creating a semi-implicit version of the sequential seventh order Runge-Kutta which is solved through nine stages. The parallelization simulation implementation uses the Ray module in the Python programming language by giving a 0.01 second delay for each completed stage. Comparison of the calculation of the parallel model and the sequential model in terms of accuracy shows the same results, even in some cases, parallel is better. It is generally seen that the parallel method will approach the analytical solution by increasing the number of iterations. In terms of execution time, parallel method has advantage over sequential method.