IJPAM: Volume 13, No. 3 (2004)

INHOMOGENEOUS HEAT-CONDUCTION PROBLEMS
SOLVED BY A NEW EXPLICIT FINITE
DIFFERENCE SCHEME

Matej Praprotnik$^1$, Marjan Šterk$^2$, Roman Trobec$^3$
$^1$National Institute of Chemistry
Hajdrihova 19, SI-1001, Ljubljana, SLOVENIA
e-mail: [email protected]
$^{2,3}$Jozef Stefan Institute
Jamova 39, SI-1000, Ljubljana, SLOVENIA
$^2$e-mail: [email protected]
$^3$e-mail: [email protected]


Abstract.A heat conduction in systems composed of biomaterials, such as the heart muscle, is described by the familiar heat conduction equation. Due to the inhomogeneity of these materials the equations defining the diffusion problem are difficult to solve. A new explicit finite difference scheme for solving the heat conduction equation for inhomogeneous materials is derived. The new scheme has the same computational complexity as the standard scheme and gives the same solution but with increased resolution of the temperature grid. It was derived and studied on a simple one dimensional problem of heat conduction and applied to studying the temperature distribution in a three dimensional model of the heart muscle.

Received: January 29, 2004

AMS Subject Classification: 80A20, 65N06

Key Words and Phrases: heat conduction equation, finite difference scheme, inhomogeneous materials, heart muscle simulation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 3