Comparison Numerical Solution of ODE

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The exact general solution of the example is . Inputting the initial value gives and the particular solution is . From initial value, this solution only exist in the range up to about because beyond that the right hand side is negative and square root of negative number give complex number.

Plot of all the four Runge-Kutta method and the exact solution is given below

Note that the numerical solutions of the four methods produce almost the same results bit there is still gap between the numerical solution and the exact solution. Depending on the problem, this gap usually can be narrowed by setting smaller value of .

Though the exact solution does not exist after , the numerical solutions still produce some results but the four methods produce different results. Care must be taken to ensure that you use the domain that produces solution.

Comments for this tutorial

See also: Numerical Excel tutorial, Dynamical System tutorial, Kardi Teknomo's Tutorial

This tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi. Solving Ordinary Differential Equation (ODE). http:\\people.revoledu.com\kardi\ tutorial\ODE\

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