On approximate solutions of the diffusion and convection-diffusion equations

Bu makalede, lineer ve lineer olmayan diffizyon ve konveksiyon diffizyon denklemlerinin çözümü için ayrışım metodu kullanıldı. Bu problemlerin yaklaşık çözümleri kolaylıkla hesaplanabilen bir seri formunda bulundu. Sunulan metodun hassaslığını ölçmek için analitik, yaklaşık ve sayısal sonuçlar karşılaştırıldı. Sonuçlar gösterdi ki sunulan metod diğer sayısal metodlardan daha hassasdır. Sayısal ve sembolik hesaplamaların çoğu Matematika paket programı kullanılarak yapıldı

Diffizyon ve konveksiyon diffizyon denklemlerinin yaklaşık çözümleri üzerine

In this paper, the decomposition method is implemented for solving the linear and nonlinear diffusion and convection-diffusion equations. The approximate solutions of these problems are calculated in the form of a series with easily computable components. The accuracy of the proposed numerical scheme is examined by comparison with analytical, approximate and numerical results. The results show that the present method is more accuracy than other numerical methods. Most of the symbolic and numerical computations have been performed using the Computer Algebra System-Matematica.

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1.G.Adomian, Nonlinear stochastic systems theory and applications to physics, Kluwer, Dordrech, Holland, 1989.
2.G.Adomian, Solving frontier problems of physics: The decomposition method, Kluwer Academic Press, Boston, 1994.
3.G.Adomian,, Comput. Math. Applic, 21(1989) 101.
4.M.Inc and D.J.Evans, Intern. J. Computer Math., 81 (2004) 685.
5.M.Inc, Y.Cherruault and K.Abbaoui, Kybernetes, 33 (2004) 80.
6.M.Inc and Y.Cherruault, Kybernetes, 32 (2003) 1492.
7.M.Inc and Y.Cherruault, Kybernetes, 31 (2002) 536.
8.M.Inc, Appl. Math. Comput., in press.
9.M.Inc and M.Isık, J. Analysis, 11 (2003) 43.
10.M.Inc, M.Ergüt and D.J.Evans, IJSPM, in press.
11.A.M.Wazwaz, Chaos, Solitons and Fractals, 12 (2001) 1549.
12.V.Seng, K.Abbaoui and Y.Cherruault, Math. Comput. Modelling, 24 (I) (1995) 59
13.Y.Cherruault, Kybernetes, 18 (2) (1989) 31.
14.Y.Cherruault, G.Saccomandi and B.Some, Math. Comput. Modelling, 16 (2) (1992) 85.
15.Y.Cherruault and G.Adomian, Math. Comput. Modelling, 18(12) (1993) 103.
16.N.Bellomo and D.Sarafyan, J. Math. Anal. Appl., 123 (1987) 389.
17.N.Bellomo and R.Monaco, J. Math. Anal. Appl., 110 (1985)495.
18.A.M.Wazwaz, Appl. Math. Comput, 97 (1998) 37.
19.M.M.Chawla and M.A.Al-Zanaidi, Comp. Math. Applic, 38 (1999) 51.
20.M.M.Chawla, M.A.Al-Zanaidi and M.G.AI-Aslab, Comp. Math. Applic, 39 (2000) 71.