You are required to solve Poisson equation for U(x,y): v?U = ax? ay? = 4.084 +4.689 xy in the region given by OSXS1, 0syS1 The boundary conditions are U(x,0) = 1.757(1-x), U(0,y)=1.757(1-y), U(x,1)=0, U(1,y)=0. You should use a step length of h = 1/3 for both x and y. You should approximate V2U using the usual five-point scheme. Enter the boundary conditions and your estimates for U(ih,jh) in the following table, giving your answers to 4 decimal places exactly
You are required to solve Poisson equation for U(x,y): v?U = ax? ay? = 4.084 +4.689 xy in the region given by OSXS1, 0syS1 The boundary conditions are U(x,0) = 1.757(1-x), U(0,y)=1.757(1-y), U(x,1)=0, U(1,y)=0. You should use a step length of h = 1/3 for both x and y. You should approximate V2U using the usual five-point scheme. Enter the boundary conditions and your estimates for U(ih,jh) in the following table, giving your answers to 4 decimal places exactly
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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![You are required to solve Poisson equation for U(x,y):
v?U =
= 4.084 +4.689 xy
+
in the region given by
OSx<1, 0<ys1
The boundary conditions are
U(x,0) = 1.757(1-x), U(0,y)= 1.757(1- y), U(x,1)=0, U(1,y)= 0.
You should use a step length of h = 1/3 for both x and y. You should approximate V²U
using the usual five-point scheme.
Enter the boundary conditions and your estimates for U(ih,jh) in the following table,
giving your answers to 4 decimal places exactly
j=3
j=2
j=1
j=0
i=0
i=1
i=2
i=3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa70bddda-0ae9-4119-87d3-ed528445523d%2F87cd5374-5b8c-4bf2-858a-3a437f1168fe%2F2aireg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:You are required to solve Poisson equation for U(x,y):
v?U =
= 4.084 +4.689 xy
+
in the region given by
OSx<1, 0<ys1
The boundary conditions are
U(x,0) = 1.757(1-x), U(0,y)= 1.757(1- y), U(x,1)=0, U(1,y)= 0.
You should use a step length of h = 1/3 for both x and y. You should approximate V²U
using the usual five-point scheme.
Enter the boundary conditions and your estimates for U(ih,jh) in the following table,
giving your answers to 4 decimal places exactly
j=3
j=2
j=1
j=0
i=0
i=1
i=2
i=3
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