Finite Difference Method
30.1 Introduction
As we have seen, weighted residual methods form a class of methods that can be used to solve differential equations. They make use of approximation functions that are appropriately weighted in order to find a solution which approximates the solution to the differential equations as closely as possible. Weighted residual methods are used in several other commonly encountered methods for solving differential equations numerically, mostly FVM and FEM.
Before introducing these methods, we will quickly introduce the finite difference method (FDM). We have (indirectly) worked with FDM already, as it forms the basis for most of the numerical schemes we used in section 25.
The concept of FDM is focused ...
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