Closed Form Discrete Numerical Solution of Diffusion Problems with Space Varying Properties and Source Term

Name: Closed Form Discrete Numerical Solution of Diffusion Problems with Space Varying Properties and Source Term
Start: 2004-06-21T00:00:00Z
Location: 5th Pan-American Workshop, Applied and Computational Mathematics and Engineering, Tegucigalpa, Honduras

Lucas Jódar Sánchez, Luz Angélica Caudillo Mata

Date

Jun 21, 2004

Event

5th Pan-American Workshop, Applied and Computational Mathematics and Engineering

Location

5th Pan-American Workshop, Applied and Computational Mathematics and Engineering, Tegucigalpa, Honduras

Tegucigalpa,

This paper deals with the construction of closed form discrete numerical solutions of diffusion mixed problems with space varying properties and source term of the form

$r(x)u_t=[p(x)u_x]x + q(x)u= F(x,t)$ (1)
$u_x(0,t)-h1 u(0,t)=0, t>0$ (2)
$u_x(1,t)-h2 u(1,t)=0, t>0$ (3)
$u(x,0)=f(x), 0\leq x \leq 1$ (4)

Coefficients $p(x)$, $r(x)$ and constants $h1, h2$ are positive, while $q(x)$ and $F(x,t)$ are real numbers. After discretization of the problems (1)-(4), an eigenfunction method is developed to obtain a closed form solution of the discretized problem. The proposed approach has the advantage that the proposed closed form formula is applicable for any source term $F(x,t)$. An algorithm is proposed and stability properties and examples are also included.