Differential Equations Lecture Work Solutions 314

Differential Equations Lecture Work Solutions 314 - 1 Apply...

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1. Apply the ADI scheme to the 2-D heat equation and find u n +1 at the internal grid points in the mesh shown in figure 60 for r x = r y = 2 . The initial conditions are u n = 1 x 3∆ x along y = 0 u n = 1 y 2∆ y along x = 0 u n = 0 everywhere else and the boundary conditions remain fixed at their initial values. Step 1: u n +1 / 2 i j u n i j = r x 2 =1 u n +1 / 2 i +1 j 2 u n +1 / 2 i j + u n +1 / 2 i 1 j + r y 2 =1 u n i j +1 2 u n i j + u n i j 1 Step 2: u n +1 i j u n +1 / 2 i j = r x 2 =1 u n +1 / 2 i +1 j 2 u n +1 / 2 i j + u n +1 / 2 i 1 j + r y 2 =1 u n +1 i j +1
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