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So far, Fourth Order Runge-Kutta is the most popular and widely used. For many practical purposes, you may use this solution.

Suppose we have ODE then

Formula :

Where

Error term : , correct up to the third order term in Taylor series expansion

The computation is using spreadsheet that can be downloaded here

Example:

, set , with initial condition . The few first results and the graph of solution are given below.

Note that after , the solution is not correct. See Comparison .

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

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This tutorial is copyrighted .

Preferable reference for this tutorial is

Teknomo, Kardi (2015) Solving Ordinary Differential Equation (ODE). http:\\people.revoledu.com\kardi\tutorial\ODE\