Numerical Analysis, 1/e

9

Initial Value Problems for Ordinary Differential Equations

9.0 INTRODUCTION

Many problems in science and engineering can be reduced to the problem of solving differential equations satisfying certain conditions. For example, spring-mass systems, resistor- capacitor-inductance circuits, bending of beams, chemical reactions, pendulums, simple harmonic motions, the motion of a rotating mass and so on. Using analytical methods we can solve only standard types of differential equations. But the differential equations appearing in practical problems of engineering and science are not of the standard types and are complex. So, it is rather impossible to find closed form solutions. Such equations are solved by numerical methods where the solution ...