Solving Ordinary Differential Equation (ODE)

By Kardi Teknomo, PhD.

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This tutorial provides an introduction and practical approach to solve Ordinary Differential Equation (ODE) by integration and numerically using Euler and Runge-Kutta methods. Many examples are given by either hand computation or numerically using mere MS Excel

In many engineering and scientific situation we face a problem that involve a rate of change. If the rate of change is a continuous function of one variable, we have ordinary differential equation (ODE). I hope you have studied at least a first year college calculus to be able to read this tutorial smoothly.

The topics of this tutorial are as follow.

What is Ordinary differential Equation (ODE)?

Solving ODE Numerically

Numerical Solution to Solve ODE

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

How to use the Spreadsheet

Comments for this tutorial

See also: Numerical Excel tutorial, Dynamical System tutorial, Kardi Teknomo's Tutorial

This tutorial is copyrighted.

Preferable reference for this tutorial is

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