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# lect_17 - Boundary Value Problems Finite Difference Methods...

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Boundary Value Problems Finite Difference Methods Boundary Conditions with Derivatives Difference Equations Central Difference N N+1 N-1 General Boundary Conditions Add extra point - N equations, N unknowns Finite Difference Representation O(h ) 4 O(h ) 2 Central Difference O(h ) 3 Backward Difference Numerical Marine Hydrodynamics Lecture 17 2.29

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Numerical Marine Hydrodynamics Partial Differential Equations – PDE Classification – Hyperbolic PDEs • Finite Difference Solutions • Wave Equation – D’Alambert’s Principle – Method of Characteristics – Parabolic PDEs – Elliptical PDEs Numerical Marine Hydrodynamics Lecture 17 2.29
Partial Differential Equations A,B and C Constants Hyperbolic Parabolic Elliptic y φ ( n ) (x,y 2 ) Quasi-linear PDE φ ( n ) (x 1 ,y) φ ( n ) (x 2 ,y) φ ( n ) (x,y 1 ) Numerical Marine Hydrodynamics Lecture 17 2.29 x

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Partial Differential Equations Hyperbolic PDE Waves on a String t Initial Conditions Boundary Conditions Wave Solutions u ( L,t) u ( 0,t) u(x,0), u t (x,0)
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• Spring '07
• HenrikSchmidt
• Partial differential equation, Numerical Marine Hydrodynamics, Numerical Marine Hydrodynamics Lecture

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