Symbolic implementation of the algorithm for calculating Adomian polynomials.

DOI10.1016/S0096-3003(02)00541-6zbMath1033.65036MaRDI QIDQ1412522

D. Massart

Publication date: 25 November 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

Adomian decomposition methodMathematicagas dynamicsAdomian polynomialsPattern matchingNonlinear operatorsNonlinear evolution equation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Iterative procedures involving nonlinear operators (47J25) Gas dynamics (general theory) (76N15) First-order nonlinear hyperbolic equations (35L60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical solutions to equations with nonlinear operators (65J15) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items (13)

A reliable symbolic implementation of algorithm for calculating Adomian polynomials ⋮ A note on the Adomian decomposition method for the generalized Huxley equation ⋮ An efficient algorithm for the multivariable Adomian polynomials ⋮ Convenient analytic recurrence algorithms for the Adomian polynomials ⋮ Solving the generalized Burgers-Huxley equation using the Adomian decomposition method ⋮ Recurrence triangle for Adomian polynomials ⋮ The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Padé technique ⋮ Decomposition methods for nonlinear, non-characteristic Cauchy heat problems ⋮ Blow-up solutions obtained using the decomposition method ⋮ Solving a system of nonlinear fractional differential equations using Adomian decomposition ⋮ Padé-Sumudu-Adomian decomposition method for nonlinear Schrödinger equation ⋮ A new definition of the Adomian polynomials ⋮ Convergence of the new iterative method

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• A convenient computational form for the Adomian polynomials
• A review of the decomposition method in applied mathematics
• A study on a boundary layer equation arising in an incompressible fluid
• Solving frontier problems of physics: the decomposition method
• A new algorithm for calculating Adomian polynomials for nonlinear operators
• The decomposition method for approximate solution of the Goursat problem
• Adomian's polynomials for nonlinear operators
• Convergence of Adomian’s method applied to integral equations
• A new approach to nonlinear partial differential equations

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