Homework_5_2011

# Homework_5_2011 - CS 111 - Introduction to Computational...

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Unformatted text preview: CS 111 - Introduction to Computational Science Homework 5 Consider a domain Ω = [−1, 1] in one spatial dimension and the following linear advection equation: ∂u ∂u +c = 0, ∂t ∂x (1) where c is the velocity. We take the initial data for u to be u(x, 0) = cos(πx). In this case the exact solution at time t is given by u(x, t) = cos (π (x − ct)). 1. Using the upwind scheme, solve equation (1) with c = 1 to a ﬁnal time tﬁnal = 2. We will assume that u is periodic in space as described in class. Take a time step restriction of t = .5 x and the number of grid points equal to 100. 2. Using the upwind scheme, solve equation (1) with c = −1 to a ﬁnal time tﬁnal = 2. We will assume that u is periodic in space as described in class. Take a time step restriction of t = .5 x and the number of grid points equal to 100. What to turn in: (1) Your code; (2) On one ﬁgure plot the exact solution and the numerical solution at tﬁnal in the case where c = 1; (3) On another ﬁgure plot the exact solution and the numerical solution at tﬁnal in the case where c = −1. 1 ...
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## This note was uploaded on 12/29/2011 for the course CS 111 taught by Professor Staff during the Fall '08 term at UCSB.

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