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Abstrakty
The paper is focused on a method for solving the heat equation in a cast-mould heterogeneous domain. The discussed method makes use of the Adomian decomposition method. The derived calculations prove the effectiveness of the method for solving such types of problems.
Czasopismo
Rocznik
Tom
Strony
57--62
Opis fizyczny
Bibliogr. 21 poz., rys.
Twórcy
autor
autor
autor
- Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland, damian.slota@polsl.pl
Bibliografia
- [1] G. Adomian, Stochastic Systems, Academic Press, New York (1983).
- [2] G. Adomian, A review of the decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications, vol. 135 (1988) 501-544.
- [3] G. Adomian, Solving Frontier Problems of Physics: the Decomposition Method, Kluwer, Dordrecht (1994).
- [4] R. Grzymkowski, E. Hetmaniok, D. Słota, Wybrane metody obliczeniowe w rachunku wariacyjnym oraz w równaniach różniczkowych i całkowych, WPKJS, Gliwice (2002).
- [5] D. Lesnic, Convergence of Adomian's decomposition metod: periodic temperatures, Computers & Mathematics with Applications, vol. 44 (2002) 13-24.
- [6] S. Pamuk, An application for linear and nonlinear heat equations by Adomian's decomposition method, Applied Mathematics and Computation, vol. 163 (2005) 89-96.
- [7] A. Soufyane, M. Boulmalf, Solution of linear and nonlinear parabolic equations by the decomposition method, Applied Mathematics and Computation, vol. 162 (2005) 687-693.
- [8] A.-M. Wazwaz, Exact solutions to nonlinear diffusion equations obtained by the decomposition method, Applied Mathematics and Computation, vol. 123 (2001) 109-122.
- [9] A.-M. Wazwaz, A. Gorguis, Exact solutions for heat-like and wave-like equations with variable coefficients, Applied Mathematics and Computation, vol. 149 (2004) 15-29.
- [10] D. Lesnic, The Cauchy problem for the wave equation using the decomposition method, Applied Mathematics Letters, vol. 15 (2002) 697-701.
- [11] A.-M. Wazwaz, A reliable technique for solving the wave equation in an infinite one-dimensional medium, Applied Mathematics and Computation, 92 (1998), 1-7.
- [12] A.-M. Wazwaz, Blow-up for solutions of some linear wave equations with mixed nonlinear boundary conditions, Applied Mathematics and Computation, vol. 123 (2001) 133-140.
- [13] S. Guellal, Y. Cherruault, Application of the decomposition method to identify the distributed parameters of an elliptical equation, Mathematical and Computer Modelling, vol. 21 (1995) 51-55.
- [14] D. Lesnic, L. Elliott, The decomposition approach to inverse heat conduction, Journal of Mathematical Analysis and Applications, vol. 232 (1999) 82-98.
- [15] M.-H. Chang, A decomposition solution for fins with temperature dependent surface heat flux, International Journal Heat and Mass Transfer, vol. 48 (2005) 1819-1824.
- [16] C.-H. Chiu, C.-K. Chen, A decomposition method for solving the convective longitudinal fins with variable thermal conductivity, International Journal Heat and Mass Transfer, vol. 45 (2002) 2067-2075.
- [17] D. J. Evans, H. Bulut, A new approach to the gas dynamics equation: an application of the decomposition method, International Journal of Computer Mathematics, vol. 79 (2002) 817-822.
- [18] R. Grzymkowski, D. Słota, Stefan problem solved by Adomian decomposition method, International Journal of Computer Mathathematics, vol. 82 (2005) 851-856.
- [19] R. Grzymkowski, D. Słota, One-phase inverse Stefan problem solved by Adomian decomposition method, Computers & Mathematics with Applications, vol. 51 (2006) 33-40.
- [20] R. Grzymkowski, M. Pleszczyński, D. Słota, Application of the Adomian decomposition method for solving the Stefan problem, in Numerical Heat Transfer 2005, EUROTHERM Seminar 82, A.J.Nowak et al. (eds.), Silesian Univ. of Technology, Gliwice (2005) 249-258.
- [21] R. Grzymkowski, M. Pleszczyński, D. Słota, Comparing the Adomian decomposition method and Runge-Kutta method for the solutions of the Stefan problem, International Journal of Computer Mathematics, vol. 83 (2006) 409-417.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0072-0010