d²ud²uu(x,t) is solution to steady state 2-D heat equation, +dx² ду2-=0,with following parameters for numerical approximation:u = u(0,0), u(0,y)=0, u(1,y)=y(1-y), 0

Given data: ∂2u∂x2+∂2u∂y2=0 u00=u(0,0)u(0,y)=0u(1,y)=y(1-y) →0<y<2u(x,0)=0u(x,2)=x(1-x)…

Answered: u(x,t) is solution to steady state 2-D…

u(x,t) is solution to steady state 2-D heat equation, d'u d'u -=0,with following parameters for numerical approximation: dx² dy ² + u= u(0,0), u (0,y)=0, u(1,y) = y(1-y), 0

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Entropy

In physics, entropy means the amount of disorder or the degree of randomness associated with a thermodynamic system. The system is not self-organized when the entropy of the system is high. For instance, when a system is at an elevated temperature, its molecules are in random motion, vibrating and colliding with each other. During this scenario, the probability of finding a molecule at a particular place twice, is low. Under this circumstance, the system can be said to be in a high entropy.

Question

d²u
d²u
u(x,t) is solution to steady state 2-D heat equation, +
dx² ду2
-=0,with following parameters for numerical approximation:
u = u(0,0), u(0,y)=0, u(1,y)=y(1-y), 0<y<2, u(x,0)=0, u(x,2) = x(1-x), 0<x<1, mesh size =0.5.
00
a. Write the approximate difference equation for this equation.
b. Calculate the point u (0.5, 1). (You don't need any computer programming here, you can calculate this by hand)

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