lecture2 - Finite Difference Representation The ultimate...

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Finite Difference Representation The ultimate goal for the solution of a PDE over a continuous domain is to reduce it to discrete model which are suitable for high speed computers. One of the standard approach is using Finite Difference Methods which are applicable to all type of second order PDE.The main steps in this approach are as follows: 1. Discretization 2. Replacing the derivatives by FD representation 3. Solving the corresponding Difference equations to get the numerical values of ‘u’ at the discretized nodes The first and third point will be discussed later. Let us discuss the approximation of the partial derivatives by corresponding Finite Differences. Let u(x, y) be the dependent variable .The Taylor’s series expansion can be written as: 2 2 2 ) , ( 2 ) ( ) , ( ) , ( ) , ( x y x u x x y x u x y x u y x x u Retaining terms upto first order,we have, ) ( ) , ( ) , ( x O x y x u y x x u x u
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lecture2 - Finite Difference Representation The ultimate...

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