Third Order Runge-Kutta Method (RK3) to Solve ODE

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Suppose we have ODE then

Formula:

Where

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

The Taylor series expansion is

Example:

, set , with initial condition . The computation is using spreadsheet that can be downloaded here. The few first results and the graph of solution are given below.

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

Comments for this tutorial

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