Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method
type: Item
instance of: scholarly article
title: Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method
zbMATH Open document ID: 1291.35026
DOI: 10.1155/2013/380484
author: Abdon Atangana
author: Adem Kilicman
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as \(N\) tends to infinity.
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 6306711
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/380484
OpenAlex ID: W1966507090
Wikidata QID: Q58916102
cites work: High-Order Finite-Differences Schemes to Solve Poisson's Equation in Polar Coordinates
cites work: \(B\)-spline approximation and fast wavelet transform for an efficient evaluation of particular solutions for Poisson's equation
cites work: High-order compact solvers for the three-dimensional Poisson equation
cites work: Multigrid method and fourth-order compact difference discretization scheme with unequal meshsizes for 3D Poisson equation
cites work: Fast multipole method for the biharmonic equation in three dimensions
cites work: A new coupled approach high accuracy numerical method for the solution of 3D non-linear biharmonic equations
cites work: High accuracy solution of three-dimensional biharmonic equations
cites work: New indirect scalar boundary integral equation formulas for the biharmonic equation
cites work: A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems
cites work: Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks
cites work: An effective high order interpolation scheme in BIEM for biharmonic boundary value problems
cites work: A Galerkin boundary node method for biharmonic problems
cites work: A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains
cites work: Neural‐network‐based approximations for solving partial differential equations
cites work: A collocation method based on one‐dimensional RBF interpolation scheme for solving PDEs
cites work: Solving 2D and 3D Poisson equations and biharmonic equations by the Haar wavelet method
cites work: The time-fractional coupled-Korteweg-de-Vries equations
cites work: A generalized version of a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate using the concept of noninteger derivatives
cites work: Solving a system of fractional partial differential equations arising in the model of HIV infection of \(\mathrm{CD4}^{+}\) cells and attractor one-dimensional Keller-Segel equations
cites work: Variational iteration method for initial and boundary value problems using He's polynomials
cites work: Homotopy perturbation method for fractional Black-Scholes European option pricing equations using Sumudu transform
cites work: Application of homotopy perturbation and variational iteration methods for Fredholm integrodifferential equation of fractional order
cites work: A reliable treatment of homotopy perturbation method for solving the nonlinear Klein-Gordon equation of arbitrary (fractional) orders
cites work: Comparison between the homotopy perturbation method and the sine-cosine wavelet method for solving linear integro-differential equations
description: scientific article; zbMATH DE number 6306711