MATH 331: Numerical Solution of PDEs
(
Spring 1999)
Course Topics
Parabolic equations in one space variable (Chapter 2)
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Explicit Euler scheme (2.4)
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Truncation error (2.5)
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Convergence analysis in maimum norm (2.6)
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Convergence analysis -- Fourier method (2.7)
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Implicit Euler scheme (2.8)
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Thomas algorithm for implicit schemes (2.9)
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The weighted average method and convergence (2.10-2.11)
Parabolic equations in two and three dimensions(Chapter 3)
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Explicit Euler scheme (3.1)
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ADI method in two dimensions (3.2)
Hyperbolic equations in one space variable (Chapter 4)
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CFL condition (4.1-4.2)
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Error analyses of the upwind scheme (4.3-4.4)
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Lax-Wendroff scheme (4.5-4.6)
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Box scheme (4.7)
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Leap-frog scheme (4.8)
Consistency, convergence and stability (Chapter 5)
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Formal definitions of consistency, convergence and stability (5.1--5.4)
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Lax Equivalence Theorem (5.5)
Elliptic equations in two dimentions (Chapter 6)
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Finite difference method (6.1)
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Maximum principle and error analysis (6.2)
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Finite element method (6.7-6.8)
Iterative solution of linear algebraic equations (Chapters 7)
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Basic iterative methods (7.1-7.2)
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Fourier analysis of convergence (7.3)
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SOR method (7.4)
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Recent development of iterative methods (7.6)
Last Revised: 15
January 1997