Numerical Methods for Partial Differential Equations (PDF)

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Finite Difference Discretization of Elliptic Equations: 1D Problem (PDF)

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Finite Difference Discretization of Elliptic Equations: FD Formulas and Multidimensional Problems (PDF)

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Finite Differences: Parabolic Problems (PDF)

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Solution Methods: Iterative Techniques (PDF)

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Iterative Methods: Multigrid Techniques (PDF)

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Finite Difference Discretization of Hyperbolic Equations: Linear Problems (PDF - 1.7 MB)

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Hyperbolic Equations: Scalar One-Dimensional Conservation Laws (PDF)

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Numerical Schemes for Scalar One-Dimensional Conservation Laws (PDF)

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Finite Element Methods for Elliptic Problems; Variational Formulation: The Poisson Problem (PDF)

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Discretization of the Poisson Problem in IR¹: Formulation (PDF)

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Discretization of the Poisson Problem in IR¹: Theory and Implementation (PDF - 1.9 MB)

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FEM for the Poisson Problem in IR² (PDF)

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Numerical Methods for PDEs, Integral Equation Methods, Lecture 1: Discretization of Boundary Integral Equations (PDF - 1.0 MB)

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Numerical Methods for PDEs, Integral Equation Methods, Lecture 2: Numerical Quadrature (PDF)

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Numerical Methods for PDEs, Integral Equation Methods, Lecture 3: Discretization Convergence Theory (PDF)

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Numerical Methods for PDEs, Integral Equation Methods, Lecture 4: Formulating Boundary Integral Equations (PDF)

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Numerical Methods for PDEs, Integral Equation Methods, Lecture 5: First and Second Kind Potential Equations (PDF)

Numerical Methods for PDEs, Integral Equation Methods, Lecture 6: Discretization and Quadrature (PDF)