Variations on a Theme of Weighted Residuals

There are five widely used variations of the method of weighted residuals for engineering and science applications. They are distinguished by the choice of the test functions, used in the minimization of the residuals (Eq. 8.8). These five methods are 

Each of these methods have attractive features, which we discuss as follows. Later, we shall concentrate on the collocation method, because it is easy to apply and it can also give good accuracy. The Galerkin method gives better accuracy, but it is somewhat intractable for higher order problems, as we illustrate in the examples to follow. 

Jhe coOocatUm method In this method the test function is the Dirac delta function at N interior points (called collocation points) within the domain of interest, say 0 x L  

If these N interior collocation points are chosen as roots of an orthogonal Jacobi polynomial of Vth degree, the method is called the orthogonal collocation method (Villadsen and Michelsen 1978). It is possible to use other orthogo- 

The subdomain method In this method the domain V of the boundary value problem is split into N subdomains Pj hence, the origin of the name subdomain method. The test function is chosen such that 

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