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A numerical treatment to the solution of quasiparabolic partial differential equations. (English) Zbl 0778.65067
Summary: This paper presents results obtained by the implementation of a hybrid Laplace transform finite element method to the solution of a 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.
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65R10 Numerical methods for integral transforms
44A10 Laplace transform
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35K15 Initial value problems for second-order parabolic equations
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[1] and , ’A low-order model for moist convection’, Tellus 38A, 381-396 (1987).
[2] ’Convolutional variational principles and methods in linear viscoelasticity’, ZAMM 54, T46-47 (1974).
[3] ’Finite element method in linear viscoelasticity’, ZAMM 54, T47-48 (1974).
[4] and , ’Zovšseobecnenie metódykonečcných prvkov pre riešsenie väzkopružzných plošsných konšstrukcií’, II.O.seminár o metode konečcn\.cych prvku, Plzeň, 121-125 (1973).
[5] Chen, Int. j. numer. methods eng. 32 pp 45– (1991)
[6] Honig, J. Comp. Appl. Math. 10 pp 113– (1984)
[7] ’Variational methods in mathematical theory of viscoelasticity’, Proceedings of EQU ADIFF III, J. E. Purkyně University Brno, Czechoslovakia, 1973, pp. 211-216.
[8] ’The use of numerical integration in FEMs for solving parabolic equations’, in (ed.), Topics in Numerical Analysis, Academic Press, London, New York, 1973, pp. 223-264.
[9] Ahlin, Math. Comp. 18 pp 264– (1964)
[10] ’Approximate methods of transform inversion for viscoelastic stress analysis’, Proc. 4th U.S. National Congress of Applied Mechanics, ASME, New York, 1962, pp. 1075-1085
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