Convenient analytic recurrence algorithms for the Adomian polynomials

DOI10.1016/j.amc.2011.01.007zbMath1214.65064OpenAlexW2065261869MaRDI QIDQ632864

Jun-Sheng Duan

Publication date: 28 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.01.007

zbMATH Keywords

differential equationnonlinear operatorAdomian decomposition methodAdomian polynomials\texttt{MATHEMATICA}recurrence algorithmssymbolic software

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Numerical aspects of recurrence relations (65Q30) Numerical methods for difference equations (65Q10)

Related Items (61)

Two reliable methods for solving the Volterra integral equation with a weakly singular kernel ⋮ Analytic approximation of Volterra's population model ⋮ Numerical solution of Riccati equations by the Adomian and asymptotic decomposition methods over extended domains ⋮ Solving nonlocal initial-boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations by the Adomian decomposition method ⋮ Thin film flow of magnetohydrodynamic (MHD) pseudo-plastic fluid on vertical wall ⋮ An optimized decomposition method for nonlinear ordinary and partial differential equations ⋮ Analytical and numerical results of fractional differential-difference equations ⋮ An efficient numerical technique for the solution of nonlinear singular boundary value problems ⋮ Recent development of Adomian decomposition method for ordinary and partial differential equations ⋮ The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations ⋮ Numerical solutions of fourth-order Volterra integro-differential equations by the Green's function and decomposition method ⋮ An efficient series solution for nonlinear multiterm fractional differential equations ⋮ A segmented and weighted Adomian decomposition algorithm for boundary value problem of nonlinear groundwater equation ⋮ Chaos Synchronization of the Fractional Rucklidge System based on New Adomian Polynomials ⋮ Correlation between Adomian and partial exponential Bell polynomials ⋮ Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations ⋮ A new numerical technique for index-3 DAEs arising from constrained multibody mechanical systems ⋮ Saigo space-time fractional Poisson process via Adomian decomposition method ⋮ The extended Laplace transform method for mathematical analysis of the Thomas-Fermi equation ⋮ Optical dromions and domain walls with the Kundu-Mukherjee-Naskar equation by the Laplace-Adomian decomposition scheme ⋮ Riesz Riemann–Liouville difference on discrete domains ⋮ New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods ⋮ A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations ⋮ Fractional differential transform method combined with the Adomian polynomials ⋮ Solving delay differential systems with history functions by the Adomian decomposition method ⋮ Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach-Adomian-meyers modified decomposition method ⋮ Solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method ⋮ Higher-order numeric Wazwaz-El-Sayed modified Adomian decomposition algorithms ⋮ On the solutions of a Stefan problem with variable latent heat ⋮ A new efficient technique for solving two-point boundary value problems for integro-differential equations ⋮ New ideas for decomposing nonlinearities in differential equations ⋮ Analytical solution of the droplet breakup equation by the Adomian decomposition method ⋮ Analytical solutions of fractional differential equations using the convenient Adomian series ⋮ Approximate solutions of fractional Riccati equations using the Adomian decomposition method ⋮ New recurrence algorithms for the nonclassic Adomian polynomials ⋮ Approximate analytical solution of the nonlinear Bethe equation ⋮ Solution of the Magnetohydrodynamics Jeffery-Hamel Flow Equations by the Modified Adomian Decomposition Method ⋮ Efficient analytic method for solving nonlinear fractional differential equations ⋮ Higher order numeric solutions of the Lane–Emden-type equations derived from the multi-stage modified Adomian decomposition method ⋮ A new algorithm based on differential transform method for solving multi-point boundary value problems ⋮ Modeling the influence of the Casimir force on the pull-in instability of nanowire-fabricated nanotweezers ⋮ Solution of the nonlinear Kompaneets equation through the Laplace-Adomian decomposition method ⋮ A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions ⋮ Solution for the nonlinear relativistic harmonic oscillator via Laplace-Adomian decomposition method ⋮ Solution of the nonlinear Schrödinger equation with defocusing strength nonlinearities through the Laplace-Adomian decomposition method ⋮ A probabilistic approach to Adomian polynomials ⋮ Approximate solution of singular IVPs of Lane-Emden type and error estimation via advanced Adomian decomposition method ⋮ Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations ⋮ A novel computational technique for impulsive fractional differential equations ⋮ On distributions of certain state-dependent fractional point processes ⋮ A nonlinear option pricing model through the Adomian decomposition method ⋮ Fractional impulsive differential equations: exact solutions, integral equations and short memory case ⋮ Analytic approximation of the blow-up time for nonlinear differential equations by the ADM-Padé technique ⋮ Shehu-Adomian decomposition method for dispersive KdV-type equations ⋮ Thin-film flow of magnetohydrodynamic (MHD) Johnson-Segalman fluid on vertical surfaces using the Adomian decomposition method ⋮ Adomian decomposition method for solving fragmentation and aggregation population balance equations ⋮ A study on the systems of the Volterra integral forms of the Lane-Emden equations by the Adomian decomposition method ⋮ An efficient approach for solving second-order nonlinear differential equation with Neumann boundary conditions ⋮ Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method ⋮ A combined technique for computation of energy-effect of cycles in conjugated molecules ⋮ The Volterra integral form of the Lane-Emden equation: new derivations and solution by the Adomian decomposition method

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Unnamed Item
• An efficient algorithm for the multivariable Adomian polynomials
• An algorithm for Adomian decomposition method
• A convenient computational form for the Adomian polynomials
• The decomposition method for solving the coupled modified KdV equations
• Recurrence triangle for Adomian polynomials
• Partial differential equations and solitary waves theory
• On a class of nonlinear dynamical systems: the structure of a differential operator in the application of the decomposition method
• A modified decomposition
• Generalization of Adomian polynomials to functions of several variables
• A reliable modification of Adomian decomposition method
• Solving frontier problems of physics: the decomposition method
• The theoretical foundation of the Adomian method
• Convergence of Adomian's method applied to differential equations
• An alternate algorithm for computing Adomian polynomials in special cases
• A mathematical model of Adomian polynomials
• Symbolic implementation of the algorithm for calculating Adomian polynomials.
• A new algorithm for calculating Adomian polynomials for nonlinear operators
• Nonlinear equations with mixed derivatives
• Inversion of nonlinear stochastic operators
• Nonlinear stochastic differential delay equations
• A new modification of the Adomian decomposition method for linear and nonlinear operators
• Exact solutions to nonlinear diffusion equations obtained by the decomposition method
• New ideas for proving convergence of decomposition methods
• Practical formulae for the calculus of multivariable Adomian polynomials
• Non-perturbative analytical solution of the general Lotka-Volterra three-species system
• Application of the decomposition method to the solution of the reaction- convection-diffusion equation
• A reliable symbolic implementation of algorithm for calculating Adomian polynomials
• Solution of system of fractional differential equations by Adomian decomposition method
• An improvement to an alternate algorithm for computing Adomian polynomials in special cases
• A new algorithm for calculating Adomian polynomials
• Solution of systems of integral-differential equations by Adomian decomposition method
• A developed new algorithm for evaluating Adomian polynomials
• Reduced Polynomials and Their Generation in Adomian Decomposition Methods
• Convergence of Adomian's Method
• A new definition of the Adomian polynomials
• An Efficient Methodology for the Physical Sciences

This page was built for publication: Convenient analytic recurrence algorithms for the Adomian polynomials