Discretization

On the interval , we place a uniform mesh, say

To approximate on this mesh, we define a mesh function as the solution of a system of finite difference equations which are in some sense an approximation to the above problem. An obvious such difference formulation is

(10.3)

We now proceed to show that the linear system (10.3) can be solved by a simple algorithm if is sufficeintly small, and then we estimate the accuracy of this numerical solution.

Multiplying (10.3) by , we have

(10.4)