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

Francisco Edmundo de Andrade
Organization: Universidade Federal do Ceará - BRAZIL
Júlio Wilson Ribeiro
Organization: Universidade Federal do Ceará - BRAZIL
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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.

NOTE: Newer versions of the code can be downloaded from this link: https://github.com/edmundoandrade/gitt/

*Mathematics > Calculus and Analysis > Differential Equations

GITT, Hybrid Analytical-Numerical Method, Generalized, Integral Transform Technique, Eigen-values

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Citt.m (6.5 KB) - Mathematica Package
GITTSAMP.nb (161.7 KB) - Mathematica Notebook
gitt.m (7.3 KB) - Mathematica Package