Fourth Order Runge-Kutta Method to Solve ODE

Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4

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Runge Kutta-4

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 Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4 then

Formula : Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4

Where

Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4

Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4

Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4

Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4

Error term : Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4 , correct up to the third order term in Taylor series expansion

Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4

The computation is using spreadsheet that can be downloaded here

Example:

Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4 , set Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4 , with initial condition Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4 . The few first results and the graph of solution are given below.

Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4

Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4

Note that after Solving Ordinary Differential Equation (ODE) using Runge-Kutta-4 , 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\