(d) The partial differential equationa2uazu16 – x2 – 2yfor0

Given the partial difference equation, uxx+uyy=16-x2-2y, for 0<x<4, 0<y<2. Let h=k=1…

Answered: (d) The partial differential equation…

Math

Advanced Math

(d) The partial differential equation a2u a2u = 16 – x2 – 2y for 0

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

(d) The partial differential equation
a2u
azu
16 – x2 – 2y
for
0 <x < 4, 0 < y< 2
(1.1)
ду?
is subject to the boundary conditions
u(x, 0) = 0 and u(x,2) = 2(16 – x²)
for 0 <x <4
u(0, y) = y and u(4,y) = 0
for 0 < y < 2
Using centred difference approximations with a grid size ofh= 1, write the above boundary
value problem in finite difference form, Sketch the finite difference grid and input the
boundary conditions and label the unknown nodes. Hence show that the finite difference form
of equation (1.1) can be written as:
%3D
-4
1
-181
-4
U21
1
-41 Lu31-
and
U13.
Using gausse ellimination method solve above system of equations for u11, U12

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ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated