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### poisson-bak

Course: M 171, Fall 2009
School: University of Iowa
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of Rates Convergence Iteration Methods for Poisson's Equation Consider the discretization (8.8.1) of page 557 for Poisson's equation. De ne p21 ; 2 = 1 ; 2 sin2 2N ! = 1+ Rate of Convergence Jacobi Gauss-Seidel SOR For the SOR method, r ! ;1 0 ! 2 8 &lt; (M (!)) = : 1 4 ! ;1 ! + (! )2 + 4 (1 ; !) q ! ! ! 2 Let MJ , MGS , and MSOR denote number the of iterations needed to reduce the iteration...

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of Rates Convergence Iteration Methods for Poisson's Equation Consider the discretization (8.8.1) of page 557 for Poisson's equation. De ne p21 ; 2 = 1 ; 2 sin2 2N ! = 1+ Rate of Convergence Jacobi Gauss-Seidel SOR For the SOR method, r ! ;1 0 ! 2 8 < (M (!)) = : 1 4 ! ;1 ! + (! )2 + 4 (1 ; !) q ! ! ! 2 Let MJ , MGS , and MSOR denote number the of iterations needed to reduce the iteration error by a factor of 10, for the Jacobi, Gauss-Seidel, and SOR methods, respectively. 2 ! MJ MGS MSOR ;1 N = 10 :9510565 :9045085 :527864 46 23 4...

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University of Iowa - M - 171
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