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So far, Fourth Order RungeKutta 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
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\