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A new approach to solve a diffusion-convection problem. (English) Zbl 1015.65053

Summary: We use the Adomian decomposition method to study a nonlinear diffusion-convection problem (NDCP). The decomposition method has been applied recently to a wide class of nonlinear stochastic and deterministic operator equations involving algebraic, differential, integro-differential and partial differential equations and systems. The method provides a solution without linearization, perturbation, or unjustified assumptions.
An analytic solution of NDCP in the form of a series with easily computable components using the decomposition method will be determined. The non-homogeneous equation is effectively solved by employing the phenomena of the self-cancelling ‘noise terms’ whose sum vanishes in the limit. Comparing the methodology with some known techniques shows that the present approach is highly accurate.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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[1] DOI: 10.1016/0022-247X(84)90182-3 · Zbl 0554.60065
[2] DOI: 10.1016/0022-247X(86)90037-5 · Zbl 0596.60094
[3] DOI: 10.1016/S0096-3003(96)00283-4 · Zbl 0904.35078
[4] DOI: 10.1016/0898-1221(94)00144-8 · Zbl 0809.65073
[5] DOI: 10.1016/0898-1221(95)00022-Q · Zbl 0832.47051
[6] DOI: 10.1016/0022-247X(85)90178-7 · Zbl 0606.34009
[7] Adomian, G. and Rach, R. (1988), ”Coupled differential equation and coupled boundary conditionsM”, J. Math. Anal. Appl., Vol. 112, pp. 112–29.
[8] DOI: 10.1016/0898-1221(90)90246-G · Zbl 0702.35058
[9] DOI: 10.1016/0893-9659(91)90058-4 · Zbl 0742.40004
[10] DOI: 10.1016/0898-1221(92)90031-C · Zbl 0777.35018
[11] DOI: 10.1016/S0895-7177(96)00167-7 · Zbl 0874.92021
[12] DOI: 10.1016/0022-247X(85)90311-7 · Zbl 0575.60064
[13] DOI: 10.1016/0022-247X(87)90318-0 · Zbl 0624.60079
[14] DOI: 10.1016/0895-7177(93)90233-O · Zbl 0805.65057
[15] DOI: 10.1016/0895-7177(92)90009-A · Zbl 0756.65083
[16] DOI: 10.1016/0895-7177(96)00050-7 · Zbl 0854.76094
[17] DOI: 10.1016/0022-247X(87)90199-5 · Zbl 0645.60067
[18] Sincovec, R.F. and Madsen, N.K. (1975), ”Software for non-linear partial differential equations”, ACM Trans. Math. Software, p. 1. · Zbl 0311.65057
[19] DOI: 10.1016/S0030-4018(99)00630-6
[20] Van Tonningen, S. (1995), ”Adomian’s decomposition method: a powerful technique for solving engineering equations by computer”, Computers Education J., Vol. 5, No. 4, pp. 30–4.
[21] DOI: 10.1080/00207169708804617 · Zbl 0891.65105
[22] DOI: 10.1016/S0096-3003(95)00327-4 · Zbl 0882.65132
[23] DOI: 10.1016/S0096-3003(97)10127-8 · Zbl 0943.65084
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.