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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
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
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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