An algorithm for Adomian decomposition method

DOI10.1016/j.amc.2003.10.037zbMath1062.65059OpenAlexW2006004305MaRDI QIDQ702597

Zhengyi Lu, Wenhai Chen

Publication date: 17 January 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2003.10.037

zbMATH Keywords

algorithmnonlinear differential equationssymbolic computationnonlinear operator equationAdomian decomposition methodAdomian polynomials

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Iterative procedures involving nonlinear operators (47J25) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical solutions to equations with nonlinear operators (65J15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Packaged methods for numerical algorithms (65Y15)

Related Items

An algorithm for solving the high-order nonlinear Volterra-Fredholm integro-differential equation with mechanization ⋮ A mechanical algorithm for solving ordinary differential equation ⋮ A new mechanical algorithm for solving the second kind of Fredholm integral equation ⋮ Approximate analytical solution of singularly perturbed boundary value problems in Maple ⋮ Numerical study of modified Adomian's method applied to Burgers equation ⋮ Super cubic iterative methods to solve systems of nonlinear equations ⋮ Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force ⋮ A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM-Padé technique ⋮ Effects of Navier slip on a steady flow of an incompressible viscous fluid confined within spirally enhanced channel ⋮ An efficient algorithm for the multivariable Adomian polynomials ⋮ A modified Adomian method for system of nonlinear differential equations ⋮ Optical solitary waves and soliton solutions of the \((3+1)\)-dimensional generalized Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation ⋮ Solving multispecies Lotka-Volterra equations by the Daftardar-Gejji and Jafari method ⋮ Convenient analytic recurrence algorithms for the Adomian polynomials ⋮ Solving delay differential systems with history functions by the Adomian decomposition method ⋮ New ideas for decomposing nonlinearities in differential equations ⋮ Approximate analytical solutions for a mathematical model of a tubular packed-bed catalytic reactor using an Adomian decomposition method ⋮ Variational iteration method for solving multispecies Lotka-Volterra equations ⋮ Analytical solution of fractionally damped beam by Adomian decomposition method ⋮ A modified algorithm for the Adomian decomposition method with applications to Lotka-Volterra systems ⋮ New modification of the HPM for numerical solutions of the sine-Gordon and coupled sine-Gordon equations ⋮ Non-classical heat conduction problem with nonlocal source ⋮ A \texttt{Maple} package of new ADM-Padé approximate solution for nonlinear problems ⋮ Recurrence triangle for Adomian polynomials ⋮ A new iterative method to compute nonlinear equations ⋮ A mechanical algorithm for solving the Volterra integral equation ⋮ Mechanical algorithm for solving the second kind of Volterra integral equation ⋮ Blow-up solutions obtained using the decomposition method ⋮ Applying Adomian decomposition method to solve Burgess equation with a non-linear source ⋮ A new iterative method for solving nonlinear equations ⋮ Solving the nonlinear equations for one-dimensional nano-sized model including Rydberg and Varshni potentials and Casimir force using the decomposition method ⋮ Approximate analytic solutions for a two-dimensional mathematicalmodel of a packed-bed electrode using the Adomian decomposition method ⋮ A new definition of the Adomian polynomials ⋮ A comparison of numerical solutions of fractional diffusion models in finance ⋮ A nonlinear option pricing model through the Adomian decomposition method ⋮ An algorithm for solving DAEs with mechanization ⋮ An algorithm for solving nonlinear singular perturbation problems with mechanization ⋮ Computations of multi-resultant with mechanization ⋮ A two-step Adomian decomposition method ⋮ Mechanization for solving SPP by reducing order method

Uses Software

• Maple

Cites Work

• A convenient computational form for the Adomian polynomials
• A review of the decomposition method in applied mathematics
• Explicit solutions of nonlinear partial differential equations
• New results for convergence of Adomian's method applied to integral equations
• A comparison between Adomian decomposition method and Taylor series method in the series solutions
• Solving frontier problems of physics: the decomposition method
• The theoretical foundation of the Adomian method
• Convergence of Adomian's method applied to differential equations
• The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model
• A new algorithm for calculating Adomian polynomials for nonlinear operators
• Nonlinear equations with mixed derivatives
• New ideas for proving convergence of decomposition methods
• Adomian's polynomials for nonlinear operators
• Classroom Note:Numerical and Analytical Solutions of Volterra's Population Model
• A new approach to nonlinear partial differential equations
• The numerical solution of sixth-order boundary value problems by the modified decomposition method