ABSTRACT
Fortunately, there are many good methods available for solving the initial-value problem. The simplest method of all the numerical methods for ordinary differential equations is Euler’s method. In solving an initial-value problem, it is useful to distinguish two types of errors: local and global truncation errors. Of course there is always the presence of the round-off error, but the people assume that there is no round-off error involved in any of the calculations. Euler’s method was derived from the Taylor Series using two terms in the series. It should be clear that they can construct an approximate solution of the initial-value problem using a large number of terms. MATLAB toolbox contains several built-in functions for solving ordinary differential equations. The major disadvantage common to all multistep methods, in general, and Adams-Bashforth methods, in particular, is that they are not self-starting. Because of round-off error in the computer, errors are committed as the explicit calculation is carried out.
