Analytic numerical solution of coupled semi-infinite diffusion problems

• Published in: Computers & mathematics with applications (1987) Vol. 30; no. 12; pp. 1 - 10
• Main Authors: Jódar, L., Goberna, D.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1995; Elsevier
• Subjects: Analytic-numerical solution; Coupled diffusion problem; Error bound; Exact sciences and technology; Exact solution; Mathematics; Matrix functional calculus; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Coupled diffusion problem; Error bound; Matrix functional calculus; Analytic-numerical solution; Exact solution; Upper bound; Fourier transformation; Numerical solution; Matrix calculus; Diffusion equation; Functional calculus
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/0898-1221(95)00170-4

In this paper, we consider coupled semi-infinite diffusion problems of the form u t ( x, t)− A 2 u xx ( x, t) = 0, x > 0, t > 0, subject to u(0, t)= B and u( x,0)=0, where A is a matrix in C r×r , and u( x, t), and B are vectors in C r . Using the Fourier sine transform, an explicit exact solution of the problem is proposed. Given an admissible error ∈ and a domain D( x 0, t 0)={( x, t);0≤ x≤ x 0, t≥ t 0 > 0, an analytic approximate solution is constructed so that the error with respect to the exact solution is uniformly upper bounded by ∈ in D( x 0, t 0).