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Partial Differential Equations
Chapter 12 Burden and Faires 11/18/2018 PDE's
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General 2nd Order Form 11/18/2018 PDE's
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Discriminant 11/18/2018 PDE's
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Classification 11/18/2018 PDE's
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Conic Sections 11/18/2018 PDE's
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Classification 11/18/2018 PDE's
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Elliptical PDE 11/18/2018 PDE's
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Elliptical PDE 11/18/2018 PDE's
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FDM Molecule 11/18/2018 PDE's
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ODE Second Order Formula
xi-1 xi xi+1 11/18/2018 PDE's
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ODE Second Order Central Difference Formulas
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ODE Second Order Central Difference Formulas
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PDE Second Order Central Difference Formulas
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PDE Second Order Central Difference Formulas
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Example Problem Consider a square plate 0.5 m on a side. Two sides are held at 0o and two sides vary from 0 to 100o Find the steady state temperature. 11/18/2018 PDE's
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Boundary Conditions 11/18/2018 PDE's
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Mesh 4 3 2 1 j = 0 i = 11/18/2018 PDE's
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Mesh y4 y3 y2 y1 y0 x0 x x x x4 11/18/2018 PDE's
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Mesh y4 y3 y2 y1 y0 x0 x x x x4 11/18/2018 PDE's
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Notation 11/18/2018 PDE's
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PDE Second Order Central Difference Formulas
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PDE Second Order Central Difference Formulas
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Equations: 11/18/2018 PDE's
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Solution of Equations For smaller systems use a direct method.
Gaussian Elimination Matrix Factorization For larger systems use an iterative method. Gauss-Seidel Successive Over Relaxation 11/18/2018 PDE's
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Symmetric Block Tridiagonal Matrix Form
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Symmetric Block Tridiagonal Matrix Form
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Theorem 11/18/2018 PDE's
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Matrix Form 11/18/2018 PDE's
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Matrix Form 11/18/2018 PDE's
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Poisson’s Equation Problem
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PDE Second Order Central Difference Formulas
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PDE Second Order Central Difference Formulas
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Alternative Notation N W E S 11/18/2018 PDE's
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Other Topics Alternative Solution Techniques. Derivative B.C.
Nonuniform Boundaries. Alternative Coordinate systems. 11/18/2018 PDE's
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Alternative Solution Procedure
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Alternating Direct Implicit Method
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Alternating Direct Implicit Method
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Example 12 12 11/18/2018 PDE's
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Example 11/18/2018 PDE's
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Equations 11/18/2018 PDE's
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Gauss Elimination 11/18/2018 PDE's
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Gauss-Seidel 11/18/2018 PDE's
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Alternating Direct Implicit Method - Rows
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Alternating Direct Implicit Method - Columns
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Derivative B.C. Function value specified on boundary are called Dirichlet B.C. Derivative values specified on boundary are called Neumann Boundary Conditions 11/18/2018 PDE's
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Example: 11/18/2018 PDE's
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Example 11/18/2018 PDE's
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Example 11/18/2018 PDE's
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Example 11/18/2018 PDE's
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Pseudo-Nodes 11/18/2018 PDE's
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Equations 4 equations in 6 unknowns. 11/18/2018 PDE's
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Derivative B.C 11/18/2018 PDE's
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Derivative B.C 11/18/2018 PDE's
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Irregular Boundary 11/18/2018 PDE's
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FDM Molecule 11/18/2018 PDE's
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Taylor Series 11/18/2018 PDE's
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FDM 11/18/2018 PDE's
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FDM 11/18/2018 PDE's
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FDM 11/18/2018 PDE's
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FDM 11/18/2018 PDE's
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FDM 11/18/2018 PDE's
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FDM 11/18/2018 PDE's
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FDM 11/18/2018 PDE's
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FDM 11/18/2018 PDE's
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