21 - 761 Finite Difference Methods Spring 2010
نویسندگان
چکیده
4 Initial Value Problems for PDEs 18 4.1 Heat Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 FDMs for Parabolic Problems . . . . . . . . . . . . . . . . . . . . 19 4.2.1 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Mixed IVP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.3.1 Implicit Scheme . . . . . . . . . . . . . . . . . . . . . . . 23 4.3.2 Crank-Nicholson Scheme . . . . . . . . . . . . . . . . . . . 24 4.4 FDMs for Hyperbolic Equations . . . . . . . . . . . . . . . . . . . 25 4.4.1 First Order Scalar Equation . . . . . . . . . . . . . . . . . 25 4.4.2 Characteristic tracing and interpolation . . . . . . . . . . 27 4.5 The CFL Condition . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.6 Modified Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.6.1 Higher Order Methods . . . . . . . . . . . . . . . . . . . . 30
منابع مشابه
Some Stable Difference Approximations to a Fourth-Order Parabolic Partial Differential Equation
where £i = * and A = 0 -11 .1 o J' Since A AA' = 0 and A'1 = —A, (4) is a Schrodinger type system of partial differential equations, (Kreiss [6]). Richtmyer [11] and Evans [5] have derived finite difference methods for the numerical solution of Eq. (4) which are based on well-known algorithms for the numerical solution of the scalar equation , _. dv _ d"v {ö) Tt~dx~*Received February 21, 1966.
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