2. Use the appropriate Fourier Series to give the solution to the initial boundary value problems below. a. (Dirichlet Problem) b. (Neumann Problem) 1 (u₁(x,t) = — uxx(x, t), 0 0, 10 u(0,t) = u(x,t) = 0, u(x, 0) = πxx², 1 t > 0, 0 < x <π. |u₁(x,t) = uxx(x, t), 00, 10 ux (0,t) = ux (2,t) = 0, u(x, 0) = 2x, t > 0, 0 < x < 2.
2. Use the appropriate Fourier Series to give the solution to the initial boundary value problems below. a. (Dirichlet Problem) b. (Neumann Problem) 1 (u₁(x,t) = — uxx(x, t), 0 0, 10 u(0,t) = u(x,t) = 0, u(x, 0) = πxx², 1 t > 0, 0 < x <π. |u₁(x,t) = uxx(x, t), 00, 10 ux (0,t) = ux (2,t) = 0, u(x, 0) = 2x, t > 0, 0 < x < 2.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
Transcribed Image Text:2. Use the appropriate Fourier Series to give the solution to the initial boundary value problems
below.
a. (Dirichlet Problem)
b. (Neumann Problem)
1
(u₁(x,t) = — uxx(x, t), 0 <x<´‚t>0,
10
u(0,t) = u(x,t) = 0,
u(x, 0) = πxx²,
1
t > 0,
0 < x <π.
|u₁(x,t) = uxx(x, t), 0<x<2,t>0,
10
ux (0,t) = ux (2,t) = 0,
u(x, 0) = 2x,
t > 0,
0 < x < 2.
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