ENGR 516 Computational Methods for Graduate Students

ENGR 516 Computational Methods for Graduate Students Catholic University of America Assignment #7 Elliptic PDE ENGR516 Assignment #5: Two Dimensional PDEs Problem #1: Alternating Direction Implicit (ADI) Method Research and write a brief explanation of the ADI Method and solve: Two Dimensional LaPlace Equation: Electric Potential Over a Flat Plate with Point Charge !!! ?2 u(x, y) = f (x, y) for -1 = x = 1, -1 = y = 1 boundary conditions: u(x,y) = 0 for all boundaries f (0.5,0.5) = -1 f (-0.5,-0.5) = 1 elsewhere : f (x, y) = 0 Two Dimensional Temperature Diffusion: !!! 10-4 ?2 u(x, y,t) ?x2 + ?2 u(x, y,t) ?y2 ? ? ? ? ? ? = ?u(x, y,t) ?t for 0 = x = 4, 0 = y = 4 0 = t = 5000 u(x, y,0) = 0 u(x, y,t) = ey cos x - ex cos y for x = 0, x = 4, y = 0, y = 4 ! ! Present results for t= 5000 Problem #2: Crank-Nicolson Problem Solve the Two-Dimensional Temperature Problem above using Crank-Nicolson Method.

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