Accurate continuous numerical solutions of time dependent mixed partial differential problems

Authors:
L. Jódar;P. Almenar
Affiliations:
-;-
Venue:
Computers & Mathematics with Applications
Year:
1996

Citing 0
Cited 8

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Abstract

In this paper, a separation of variables method for the solution of time dependent problems of the type u"t"t = c(t)u"x"x, 0 0, subject to u(0, t) = u(p, t) = 0 and u(x, 0) = @?(x}, u"t(x, 0) = g(x) is developed. First, an exact series solution of the problem is given. Given an admissible error @e 0, and a bounded domain D(T) = {(x, t); 0 @? x @? p, 0 @? t @? T, a continuous numerical solution is constructed so that the approximation error is uniformly upper bounded by @e in D(T)