The solution of Laplace equationd'u= 0, where 0 < x < 3dx?dyand 0 < y < 2 with boundaryconditions u(x, 0) = 1,u(0, y) = 3 + y,u(x, 2) = 3 - x and taking step sizeAx = Ay = 1, is=....%3Du(3, y) = 5 – y.

Step:-1 Since we know for Laplace equation if step size h= k then ui, j=14ui+1, j + ui-1, j + ui,…

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The solution of Laplace equation d'u = 0, where 0 < x < 3 dx? and 0 < y < 2 with boundary conditions u(x, 0) = 1,

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.3: Euler's Method

Problem 1YT: Use Eulers method to approximate the solution of dydtx2y2=1, with y(0)=2, for [0,1]. Use h=0.2.

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Question

The solution of Laplace equation
d'u
= 0, where 0 < x < 3
dx?
dy
and 0 < y < 2 with boundary
conditions u(x, 0) = 1,
u(0, y) = 3 + y,
u(x, 2) = 3 - x and taking step size
Ax = Ay = 1, is=....
%3D
u(3, y) = 5 – y.

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