Use u j+1, j+ Ui, j+ 1 + U j−1, j⋆ U ¡‚ j−1 −4ui,j-0 to approximate the solution of Laplace's equation at the interior points of the given region. Use symmetry when possible. (Assume u 00= u(0, 0)., u(0, y) = 0, u(2, y) = 100y, 0< y<3 u( x, 0) = 0, u( x, 3) = 100x, 0< x < 2 mesh size: h=1 What is u(1,1)? (Insert your answer here, round your answer to closest tenth)

Use u j+1, j+ Ui, j+ 1 + U j−1, j⋆ U ¡‚ j−1 −4ui,j-0 to approximate the solution of Laplace's equation at the interior points of the given region. Use symmetry when possible. (Assume u 00= u(0, 0)., u(0, y) = 0, u(2, y) = 100y, 0< y<3 u( x, 0) = 0, u( x, 3) = 100x, 0< x < 2 mesh size: h=1 What is u(1,1)? (Insert your answer here, round your answer to closest tenth)

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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Similar questions

Find the solution u(x,y) of a Laplace equation in a rectangle 0 < x < a, 0 < y < b, the boundary and intial conditions are as follows: u(0,y) = 0, u(a,y) = f(y), for 0 < y < b u(x,0) = h(x), u(x,b) = 0, for 0 £ x £ a h(x) = (x/a)2 and f(y) = 1 – (y/b) Consider combining the solutions of two problems, one with homogeneous boundary conditions for u(a,y) = f(y) and the other with homogeneous boundary conditions for u(x,0) = h. (x)

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ISBN:

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