Partial Differential Equations part 2-Computational Physics-Lecture Slides, Slides of Computational Physics

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Stability

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CFL Condition

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Example: Wave Equation (2/2)

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Time-Independent Problems

Finite Difference Methods

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Example: Laplace Equation (1/5)

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Example: Laplace Equation (3/5)

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Example: Laplace Equation (4/5)

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Poisson equation

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Assignment-

 Poisson’s equation with following BC’sWrite a MATLAB program to solve the Dr. Hanif Durad 3

xx yy n u u xy x y u x u x x u y u y y

using h=0.5 in both x and y directions

Direct vs Iterative

 Direct methods :  find the exact solution in a finite number of steps  Robust  Usually computational expensive.  Good for small dense matrix  Iterative methods:  it is close enough to the exact solution (within error tolerance)Start with an initial “guess”, successively improve the guess until  Accuracy and Convergence Issues  Good for large sparse matrix Dr. Hanif Durad CSE245\MatrixSolverI.pdf

SystemsIterative Methods for Linear

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Example: Iterative Refinement

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Splitting

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