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Foro de Matemáticas



Análisis numérico para ecuaciones diferenciales

José
Santiago, Chile
Escrito por José Aravena Damaneé
el 18/07/2010

A 6-cm by 5-cm rectangular silver plate has heat being uniformly generated at each point at

The rate q = 1. 5 cal/cm3 ·s. Let x represent the distance along the edge of the plate of length 6

Cm and y be the distance along the edge of the plate of length 5 cm. Suppose the temperature

U along the edges is kept at the following temperatures:


U(x,O) = x(6 - x), u(x, 5) = 0, ° < x < 6,

U(O, y) = y(5 - y), u(6, y) = 0, ° < y < 5,

Where the origin lies at a comer of the plate with coordinates (0,0) and the edges lie along the

Positive x- and y-axes. The steady-state temperature u = u(x, y) satisfies Poisson's equation:


(a2u /ax2) (x, y) + (a2u/ay2) (x, y) = - (q/K') 0 < x < 6, 0< y < 5,

Where K, the thermal conductivity, is 1. 04 cal/cm·deg·s. Approx. Imate the temperature u(x, y)

Using Algorithm 12. 1 with h = 0. 4 and k = 1/3.