Spreadsheet Solution of Systems of Nonlinear Differential Equations

Abstract

This paper presents a method for obtaining numerical approximation to solutions of systems of nonlinear differential equations of one variable using spreadsheets. This solution method is simply based on effecting an integration formula in a block. The input of the block is equal to a given variable and its output is equal to the integral of that variable. The block allows the user to set the initial condition for differential equation. A nonlinear differential equation of order n is solved through a cascaded interconnection of these integration blocks to obtain the solution function and all its successive derivatives. This approach can also be used to solve a system of nonlinear differential equations with initial conditions for the functions and their derivatives. The method is easy to learn and allows a step-by-step study of the solution, and an investigation of the influence of changing one or more parameters on this solution. The graphical capabilities of spreadsheets gives the method a visual feel and allows easy comparisons between exact and numerical solutions. The method is illustrated through several examples of non-linear differential equations which demonstrate its accuracy, flexibility and simplicity.