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A numerical treatment to the solution of quasiparabolic partial differential equations
Author(s) -
Chocholaty Pavol
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620361105
Subject(s) - overdetermined system , mathematics , laplace transform applied to differential equations , laplace's equation , inverse laplace transform , laplace transform , mathematical analysis , method of fundamental solutions , partial differential equation , boundary value problem , finite element method , two sided laplace transform , boundary element method , boundary knot method , fourier transform , fourier analysis , physics , fractional fourier transform , thermodynamics
This paper presents results obtained by the implementation of a hybrid Laplace transform finite element method to the solution of quasiparabolic problem. The present method removes the time derivatives from the quasiparabolic partial differential equation using the Laplace transform and then solves the associated equation with the finite element method. The numerical inverse of the Laplace transform is realized by solving linear overdetermined systems and a polynomial equation of the k th order. Test examples are used to show that the numerical solution is comparable to the exact solution of the initial‐boundary value problem at the given grid points.