Excel Scientific and Engineering Cookbook

Chapter 11. Solving Ordinary Differential Equations

Introduction

In this chapter we’re going to focus on numerically solving ordinary differential equations using Excel.

There are many methods available for numerically solving ordinary differential equations. Solution methods for initial value problems include such standard methods as Euler's method, the improved Euler method, the Runge-Kutta method, the leap frog method, various implicit schemes, as well as various adaptive schemes. Texts on numerical methods are full of such methods.

Other classes of problems dealing with ordinary differential equations include boundary value problems and initial-boundary value problems. Methods available for boundary value problems include the shooting method and variants, the band matrix method, Richardson extrapolation, various finite difference methods, and many others.

I aim to show you a few selected methods in this chapter to show you how you might implement some of these well known methods in Excel. Numerical methods texts contain detailed descriptions of these, as well as other methods. The Excel techniques I’ll show you in this chapter will allow you to implement many of the standard methods in Excel.

11.1. Solving First-Order Initial Value Problems

Problem

You need to numerically solve a first-order differential equation of the form:

y(0) = a

Solution

This is a standard initial value problem ...