Differential Equations with Boundary-Value Problems
Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
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Chapter 15.1, Problem 5E

In Problems 5 and 6 use (6) and Gauss-Seidel iteration to approximate the solution of Laplace's equation at the interior points of a unit square. Use the mesh size h = 1 4 . In Problem 5 the boundary conditions are given; in Problem 6 the values of u at boundary points are given in Figure 15.1.6.

5. u ( 0 , y ) = 0 , u ( 1 , y ) = 100 y , 0 < y < 1 u ( x , 0 ) = 0 , u ( x , 1 ) = 100 x , 0 < x < 1

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