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

Solving Ordinary Differential Equation (ODE): Runge Kutta 3

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Runge Kutta-3

Suppose we have ODE Solving Ordinary Differential Equation (ODE): Runge Kutta 3 then

Formula : Solving Ordinary Differential Equation (ODE): Runge Kutta 3

Where

Solving Ordinary Differential Equation (ODE): Runge Kutta 3

Solving Ordinary Differential Equation (ODE): Runge Kutta 3

Solving Ordinary Differential Equation (ODE): Runge Kutta 3

Error term : Solving Ordinary Differential Equation (ODE): Runge Kutta 3 , correct up to the third order term in Taylor series expansion.

The Taylor series expansion is Solving Ordinary Differential Equation (ODE): Runge Kutta 3

The computation is using spreadsheet that can be downloaded here

Example:

Solving Ordinary Differential Equation (ODE): Runge Kutta 3 , set Solving Ordinary Differential Equation (ODE): Runge Kutta 3 , with initial condition Solving Ordinary Differential Equation (ODE): Runge Kutta 3 . The few first results and the graph of solution are given below.

Solving Ordinary Differential Equation (ODE): Runge Kutta 3

Solving Ordinary Differential Equation (ODE): Runge Kutta 3

Note that after Solving Ordinary Differential Equation (ODE): Runge Kutta 3 , 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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Preferable reference for this tutorial is

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