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Transformation of a PDE system into an ODE system by using Generalized Integral Transform Technique
Authors

Francisco Edmundo de Andrade
Organization: Universidade Federal do Ceará - BRAZIL
Júlio Wilson Ribeiro
Organization: Universidade Federal do Ceará - BRAZIL
Old MathSource #

0212-320
Revision date

2002-10-01
Description

This material was produced in 1996 as part of Edmundo's master degree course. In 2002, this material was updated to work in version 4 of Mathematica. It contains a function that transforms a PDE in an ODE system by using the Generalized Integral Transform Technique [1, 2]. It's applicable to some coupled systems of diffusion equations in the form: D[u,t] == Div[k Grad[u]] - d u + p where u is a unknown variable that depends of x,y,z and t k,d depends of x,y,z p depends of x,y,z,t The work keeps in evolution. Contact the authors for suggestions and questions. To run the sample in the notebook, you must save the packages (.m) under "AddOns\StandardPackages\Calculus" in the Mathematica installation folder.

[1] Mikhailov, M.D. and Ozisik, M.N., "Unified Analysis and Solutions of Heat and Mass Diffusion", John Wiley, New York, 1984.

[2] Cotta, R.M., "Integral Transform in Comp. Heat and Fluid Flow" CRC Press, EUA, 1993.
Subject

*Mathematics > Calculus and Analysis > Differential Equations
Keywords

GITT, Hybrid Analytical-Numerical Method, Generalized, Integral Transform Technique, Eigen-values
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Citt.m (6.5 KB) - Mathematica Package
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GITTSAMP.nb (161.7 KB) - Mathematica Notebook
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gitt.m (7.3 KB) - Mathematica Package