Solving Ordinary Differential Equation (ODE) Numerically


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Solving Ordinary Differential Equation (ODE) Numerically

Though we can solve most of ODE using calculus, sometimes, we need the numerical solution within a range of domain Solving Ordinary Differential Equation (ODE) Numerically . To solve the ODE numerically, the most widely used solution is using 4-th order Runge-Kutta method.

To be able to compare the solutions, in this tutorial I provide the formulation and examples in spreadsheet from the 1 st Order Runge Kutta method (which is famous with name Euler method) up to 4 th order Runge Kutta.

Euler Method (1st Order Runge Kutta method)

2nd Order Runge Kutta method (RK2)

3rd Order Runge Kutta method (RK3)

4th Order Runge Kutta method (RK4)

Comparisons of Four Runge-Kutta Methods

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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). http:\\people.revoledu.com\kardi\tutorial\ODE\