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Solving partial differential equations

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					Solving partial differential equations
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Q1:    Convergence table for Jacobi method:




Q2:    Chartsheet showing the ln(Nit) vs ln(N) for Jacobi method:




       Comment on slope of the line:




Solving partial differential equations
Solution sheet Lent 2012                                            Page 1 of 6
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Q3:    Convergence table for Gauss—Seidel method:




       Comparison of convergence rate of Jacobi and Gauss—Seidel methods:




Q4(a): Chartsheet showing the (xi,0.5) vs xi plot for the case =0.2



       As the number of iterations increases the plot behaves in the following way:




Solving partial differential equations
Solution sheet Lent 2012                                                  Page 2 of 6
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Q4 (b):       Chartsheet showing the (xi,0.5) vs xi plot for the case =1.8



       As the number of iterations increases the plot behaves in the following way:




Q5:    Convergence table for Gauss—Seidel method with relaxation




       The Gauss—Seidel method converges fastest for a value:


       Comment on the effect of over-relaxation on the Gauss—Seidel method:

       What happens for the Gauss—Seidel method when =2.5? Answer:




Solving partial differential equations
Solution sheet Lent 2012                                                   Page 3 of 6
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Q6:    Does the iteration converge for any  value greater than 1? Answer:

       Convergence table for Jacobi method with relaxation




Q7:    Chartsheet showing the (xi,0.5) vs xi plot with over-relaxation:




       The value of  I used is

       The value of Nit I used is




Solving partial differential equations
Solution sheet Lent 2012                                                   Page 4 of 6
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Q8(a): Picture of cells A1:R61




Solving partial differential equations
Solution sheet Lent 2012                 Page 5 of 6
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Q8(b): Picture of cells A62:R83




Solving partial differential equations
Solution sheet Lent 2012                 Page 6 of 6

				
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posted:11/27/2011
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