4. The Forward-Difference method for solving ut = a²uxx is Uį,j+1 = (1 − 2λ)U¡‚j + λ[Ui+1,j + Ui−1,j]. Now modify this to write out a formula for approximate the parabolic partial differential equation ut = a²uxx + F(x), 0 0. a² At Still use λ = in your formula. (Δx)2
4. The Forward-Difference method for solving ut = a²uxx is Uį,j+1 = (1 − 2λ)U¡‚j + λ[Ui+1,j + Ui−1,j]. Now modify this to write out a formula for approximate the parabolic partial differential equation ut = a²uxx + F(x), 0 0. a² At Still use λ = in your formula. (Δx)2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![¡s Ui₁j+1
a²uxx ¡s Uį,j+1 = (1 − 2A)U¡‚j + A[Ui+1‚j + Ui-1,j].
2λ)Uį,j
Now modify this to write out a formula for approximate the parabolic partial differential equation
ut = a²uxx + F(x),
Ut
0 < x <l, t > 0.
4. The Forward-Difference method for solving ut = a²uxx
Still use λ =
a² At
(Ax)²
in your formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd83c3ce1-cd72-4e3b-8702-f62923bac270%2F040699af-723a-4ceb-88b5-2409a0b9e5f9%2F4uxrxlj_processed.png&w=3840&q=75)
Transcribed Image Text:¡s Ui₁j+1
a²uxx ¡s Uį,j+1 = (1 − 2A)U¡‚j + A[Ui+1‚j + Ui-1,j].
2λ)Uį,j
Now modify this to write out a formula for approximate the parabolic partial differential equation
ut = a²uxx + F(x),
Ut
0 < x <l, t > 0.
4. The Forward-Difference method for solving ut = a²uxx
Still use λ =
a² At
(Ax)²
in your formula.
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