Consider the backward difference method for solving the heat equation ut = Uxx un+1 2u7+1 h...
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Consider the backward difference method for solving the heat equation ut = Uxx un+1 2u7+1 h² k LTE un = n+1 Ui+l where k is the time step and h is the grid spacing. The local truncation error, denoted by LTE, of this method is given by the equation n+1 + U₁-1 u(i,©n+1) − u(i,n) (i+1, n+1) − 2u(2i,€n+1)+u(2i-1,€n+1) k 1 h² (1) where u(x, t) denotes the exact solution to the heat equation. Using equation (1), write down an expression for the local truncation error. What is the order of accuracy of this method? Consider the backward difference method for solving the heat equation ut = Uxx un+1 2u7+1 h² k LTE un = n+1 Ui+l where k is the time step and h is the grid spacing. The local truncation error, denoted by LTE, of this method is given by the equation n+1 + U₁-1 u(i,©n+1) − u(i,n) (i+1, n+1) − 2u(2i,€n+1)+u(2i-1,€n+1) k 1 h² (1) where u(x, t) denotes the exact solution to the heat equation. Using equation (1), write down an expression for the local truncation error. What is the order of accuracy of this method?
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Related Book For
Fundamentals Of Heat And Mass Transfer
ISBN: 9780470501979
7th Edition
Authors: Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera, David P. DeWitt
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