Biazar, J.; Babolian, E.; Kember, G.; Nouri, A.; Islam, R. An alternate algorithm for computing Adomian polynomials in special cases. (English) Zbl 1027.65076 Appl. Math. Comput. 138, No. 2-3, 523-529 (2003). Summary: We introduce an alternate algorithm for computing Adomian polynomials, and present some examples to show the simplicity and efficiency of the new method. Cited in 2 ReviewsCited in 38 Documents MSC: 65J15 Numerical solutions to equations with nonlinear operators 35K05 Heat equation 45G15 Systems of nonlinear integral equations 65R20 Numerical methods for integral equations 47J25 Iterative procedures involving nonlinear operators 35L60 First-order nonlinear hyperbolic equations 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs Keywords:decomposition method; numerical examples; nonlinear operator equations; nonlinear first order hyperbolic equation; diffusion equation; system of nonlinear integral equations; algorithm; Adomian polynomials PDFBibTeX XMLCite \textit{J. Biazar} et al., Appl. Math. Comput. 138, No. 2--3, 523--529 (2003; Zbl 1027.65076) Full Text: DOI References: [1] Adomian, G.; Adomian, G. E., A global method for solution of complex systems, Math. Model., 5, 521-568 (1984) · Zbl 0556.93005 [2] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic publishers: Kluwer Academic publishers Dordrecht · Zbl 0802.65122 [3] Adomian, G.; Sarafyan, D., Numerical solution of differential equations in the deterministic limit of stochastic theory, Appl. Math. Comput., 8, 111-119 (1981) · Zbl 0466.65046 [4] Gabet, L., The theoretical foundation of Adomian method, Comput. Math. Appl., 27, 12, 41-52 (1994) · Zbl 0805.65056 [5] Abbaoi, K.; Cherruault, Y.; Seng, V., Practical formula for the calculus of multivariable Adomian polynomials, Math. Comp. Model., 22, 1, 89-93 (1995) · Zbl 0830.65010 [6] Wazwaz, A. M., A new algorithm for calculating Adomian polynomials for non-linear operators, Appl. Math. Comput., 111, 53-69 (2000) · Zbl 1023.65108 [7] Babolian, E.; Biazar, J., Solution of a system of nonlinear Volterra integral equations of the second kind, Far East J. Math. Sci., 2, 6, 935-945 (2000) · Zbl 0979.65123 [8] Seng, V.; Abbaoui, K.; Cherruault, Y., Adomian’s polynomials for nonlinear operators, Math. Comp. Model., 24, 1, 59-65 (1996) · Zbl 0855.47041 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.