Numerical Solution of Initial-Value Problems
An nth-order differential equation is accompanied by n auxiliary conditions, which are required in order to determine the n constants of integration that arise in the general solution. When these conditions are provided at the same initial value of the independent variable, we have an initial-value problem (IVP). In other situations, these auxiliary conditions are specified at different values of the independent variable. And since these values are usually stated at the extremities of the system, these types of problems are referred to as boundary-value problems (BVPs).
In this chapter, we will present various methods to numerically solve initial-value problems. Stability ...
