Higher Order Runge-Kutta Method for Solving System of Ordinary Differential Equations Using MS Excel

Abstract

The real world problems are often hard to understand when data is scattered or not logically organized in a way that is conducive for us. These problems are obtained from physical and scientific phenomena and are modelled in terms of differential equations. The differential equations, solved numerically, are often implemented on simulation and computational tools. This requires programming skills. Excel spreadsheet has been used frequently for statistical analysis, however, it is rarely used for computation in mathematics, instead of having great usability and usefulness. It also easily enables a non-programmer to perform programming-like tasks in a visual tabular pen and paper approach. Many physical phenomena are modelled in terms of odes and PDEs, therefore, solving these equations, by cooperative iterative methods, is very important. There are several iterative methods, among which Euler and Runge-Kutta are the most famous ones for solving the differential equations as well as system(s) of the differential equation(s). Euler’s method has slow convergence; therefore, methods of a higher order of accuracy are often needed. Since the iterative methods manually with pen-paper are quite tedious and laboring because it involves numerous repetitive calculations. In this paper, the Excel spreadsheet is applied to solve the system of ordinary differential equations by applying the RK5 methods. It is demonstrated that the Excel spreadsheet method is faster and the solutions can be visualized by small or large alterations in the variables.