Analytic numerical solution of coupled semi-infinite diffusion problems

✍ Scribed by L. Jódar; D. Goberna

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 437 KB
• Volume: 30
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(95)00170-4

✦ Synopsis

In this paper, we consider coupled semi-infinite diffusion problems of the form ut(x, t)-A2uxx (x,t) = 0, x > 0, t > 0, subject to u(0, t) = B and u(x,O) = O, where A is a matrix in C r×r, and u(x, t), and B axe vectors in C r. Using the Fourier sine transform, an explicit exact solution of the problem is proposed. Given an admissible error e and a domain D(xo, to) = {(x,t); 0 < x < x0, t > to > 0}, an analytic approximate solution is constructed so that the error with respect to the exact solution is uniformly upper bounded by e in D(xo, to).