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Triangular Pulse

Let u(x; y) be the solution on 0 < x < 2 and 0 < y < 2 of uxx + uyy = 0
with u(0, y) = u(2, y) = u(x, 2) = 0 and u(x, 0) = f(x) the triangular pulse with f(0) = f(2) = 0 and f(1) = 2.
f(x) = {2x 0<x<1
{-2x+4 1<x<2
Let uj,k = u(j/2; k/2) for j = 1; 2; 3 and k = 1; 2; 3 as obtained by the numerical
method.
(a) Write the linear equations for the 9 unknowns u11 ; : : : ; u33 in matrix form.
(b) Use symmetry to reduce these to six equations.
(c) Solve the equations to obtain the 9 unknowns u11 ; : : : ; u33.

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Solution Summary

A triangular pulse is investigated. The solution is detailed and well presented.

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