The following partial differential equation a²U = a ax². du Ət Find the finite difference approximation equation and write the computational molecule on the above differential equation for the following discretization schemes. au at - -U₁.j+2 +4U₁, j+1=3U₁₂j₁ 2At Ui-1.j+2-2U₁j+2 +U₁+1₁j+2 (Ax)² course involved: numerical method

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question:
The following partial differential equation
a²U
Əx².
du
Ət
= a
Find the finite difference approximation
equation and write the computational
molecule on the above differential equation
for the following discretization schemes.
au
at
a²u
−U₁.j+2 +4U₁, j+1−3U₁.j
2At
Ui-1.j+2-2Ui,j+2 +Ui+l₁j+2
(Ax)²
course involved: numerical method
Transcribed Image Text:Question: The following partial differential equation a²U Əx². du Ət = a Find the finite difference approximation equation and write the computational molecule on the above differential equation for the following discretization schemes. au at a²u −U₁.j+2 +4U₁, j+1−3U₁.j 2At Ui-1.j+2-2Ui,j+2 +Ui+l₁j+2 (Ax)² course involved: numerical method
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