Question

Question #7:- Solve the Laplace equation $\nabla^2u = 0$, in the square region with mesh points and boundary conditions shown in the figure. 20 10 $u_1$ $u_2$ 30 80 $u_3$ $u_4$ 40 70 50 60 Dr. Jamil Book Series 1 Page 37 Applied Numerical Methods CH#6 Numerical PDE & Optimization Answer:- $u_1 = 1208.3, u_2 = 791.7, u_3 = 1041.7, u_4 = 458.4$

          Question #7:-
Solve the Laplace equation $\nabla^2u = 0$, in the square region with mesh points and boundary
conditions shown in the figure.
20
10
$u_1$
$u_2$
30
80
$u_3$
$u_4$
40
70
50
60
Dr. Jamil Book Series 1
Page 37
Applied Numerical Methods
CH#6
Numerical PDE & Optimization
Answer:-
$u_1 = 1208.3, u_2 = 791.7, u_3 = 1041.7, u_4 = 458.4$

Question #7:-
Solve the Laplace equation ∇^2u = 0, in the square region with mesh points and boundary
conditions shown in the figure.
20
10
u1
u2
30
80
u3
u4
40
70
50
60
Dr. Jamil Book Series 1
Page 37
Applied Numerical Methods
CH#6
Numerical PDE Optimization
Answer:-
u1 = 1208.3, u2 = 791.7, u3 = 1041.7, u4 = 458.4

Added by Monica W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shu-Ting Huang

01/09/2022

Step 1

This means that the solution u is a constant value throughout the square region. Show more…

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Question # 7:- Solve the Laplace equation grad^(2)u=0, in the square region with mesh points and boundary conditions shown in the figure. Dr. Jamil Book Series I Page 37 Applied Numerical Methods CH#6 Numerical PDE & Optimization Answer:- u1=1208.3, u2=791.7, u3=1041.7, u4=458.4 Question # 7:- Solve the Laplace equation 2u = 0, in the square region with mesh points and boundary conditions shown in the figure. 20 10 u1 u2 30 80 u3 u4 40 70 50 60 Dr. Jamil Book Series Page 37 Applied Numerical Methods CH#6 Numerical PDE & Optimization Answer:- u1=1208.3, u2=791.7, u3=1041.7, u4=458.4