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

Abstract

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, so solving these types of equations, by cooperative iterative methods, are very important there are several iterative methods. The Euler and Runge-Kutta are the most famous ones among the numerical methods 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. The spreadsheet technique in Excel is in cooperated to solve the system of an ode by applying the RK5 methods, but one of the pitfalls of an excel spreadsheet is that it is limited containing less than 256 variables (columns) and 65536 records (rows).

Convergence rate for the hybrid iterative technique to explore the real root of nonlinear problems

“…A standard convergence scheme is adopted with a class of iterative procedural manners and applications for the methods [6]. Analysis for the NITs could converge or diverge at the initial guesses; if the technique is converged, then it should be repeated until the requisite or less than requisite accuracy (accuracy estimated by error methodologies) is obtained; if the technique has diverged, it should be terminated because there could not have any solution [7][8]. Contemplate NITs to find an approximate root of ( ) 0 fx= , where : fD → for the bracketing interval D is a scalar function.…”