ABSTRACT
This chapter deals with numerical solution of ordinary differential equations and provides several simple examples of initial and boundary value problems. It also provides several examples that illustrate the important concept of the grid and that of the grid function – the trace, or projection, [u]h of the continuous solution u(x) onto the grid. The primary objective is to study the techniques for the construction and analysis of convergent schemes for ordinary differential equations. The chapter discusses verification of convergence for a difference scheme. It defines the concept of consistency, and explains what it actually means when we say that the finite-difference scheme.
