Advanced Engineering Mathematics, 7th Edition

6.3 Multistep Methods

INTRODUCTION

Euler’s, the improved Euler’s, and the Runge–Kutta methods are examples of single-step or starting methods. In these methods each successive value y_{n + 1} is computed based only on information about the immediately preceding value y_n. On the other hand, multistep or continuing methods use the values from several computed steps to obtain the value of y_{n + 1}. There are a large number of multistep method formulas for approximating solutions of DEs, but since it is not our intention to survey the vast field of numerical procedures, we will consider only one such method here.

Adams–Bashforth–Moulton Method

The multistep ...