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Unformatted text preview: ρ <1 . • The equation comes with boundary conditions: • We can discretize them as: Incorporating the Boundary Conditions • Note that the above implies ? °, ± = ? °, 0 = ²(°) . This use of ³(±) approximation leads to low accuracy. • An alternative is to use ´ µ,¶ −´ µ,−¶ 2¶ to replace ? ? : ´ µ,¶ −´ µ,−¶ 2¶ = 0 . So, ? °, ± = ? °, ·± . • Use this in (when ¸ = 0 ): 10/24/2011 Math Modeling II (Fall 2009, Xin Li) 4 Second order to first order • We can transform the wave equation to a first order system of equations (of hyperbolic type) • Let • Then • In matrix notation • Now, ideas used for advection equation can be used. Homework 1. P. 604: 1 You are supposed to use the finite difference scheme, not any analytic solution. 2. P.604: 2 This should be quick and uses the chain rule. 3. P.604: 4 More differentiation....
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 Fall '11
 Xli
 Partial differential equation, finite difference, Finite difference method, Finite differences, Numerical differential equations, advection equation

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