Results 31 to 40 of about 334 (167)

Resolution of nonlinear and non-autonomous ODEs by the ADM using a new practical Adomian polynomials

Bulletin of Computational Applied Mathematics, 2020
In this paper, a new practical formulas of Adomian polynomials has been adapted to resolve nonlinear and non-autonomous ordinary differential equations by the Adomian decomposition method, a simple computational for this new polynomials has been ...
Idriss Noureddine Zaouagui, Toufik Badredine   +1 more
doaj  

Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations

Abstract and Applied Analysis, 2012
We develop a method to obtain approximate solutions of nonlinear system of partial differential equations with the help of Sumudu decomposition method (SDM).
Hassan Eltayeb, Adem Kılıçman
doaj   +1 more source

Application of an efficient analytical technique based on Aboodh transformation to solve linear and non-linear dynamical systems of integro-differential equations

Partial Differential Equations in Applied Mathematics
In literature, it is usually very difficult to investigate the analytical and numerical solutions of fractional integro-differential equations (FIDEs). In the current work, the solutions to linear and non-linear FIDEs and their systems have been analyzed
Qasim Khan, Anthony Suen, Hassan Khan
doaj   +1 more source

A Detailed and Comprehensive Account of Fractional Physics‐Informed Neural Networks: From Implementation to Efficiency

Artificial Intelligence for Engineering, EarlyView.
Caputo‐based fPINNs accurately solve fractional ODEs and PDEs while exposing an accuracy–cost trade‐off driven by the history‐dependent fractional derivative. Temporal collocation and shorter time windows are the most effective strategies for improving early‐time accuracy without unnecessary spatial refinement.
Donya Dabiri, Joshua DaRosa, Milad Saadat, Deepak Mangal, Safa Jamali   +4 more
wiley   +1 more source

Adomian polynomials method for dynamic equations on time scales

Advances in the Theory of Nonlinear Analysis and its Application, 2021
In a recent paper, a series solution method based on combining the Laplace transform and Adomian polynomial expansion was proposed to find an approximate solution of nonlinear differential equations \cite{FA2016}. It uses the expansion in Adomian polynomials defined in \cite {A1,A2}.
Svetlin GEORGİEV, İnci M. ERHAN
openaire   +3 more sources

New Generalised Semi‐Analytical Approach for the Multidimensional Nonlinear Collisional Fragmentation Equations

International Journal for Numerical Methods in Fluids, Volume 98, Issue 8, Page 980-999, August 2026.
This work aims to develop a generalised and efficient semi‐analytical method that combines the Laplace decomposition method with Pade approximation (LDMPA) to solve multidimensional nonlinear integro‐partial differential equation. For a one‐dimension case, explicit (closed‐form) solutions for the number density functions are derived for the first time.
Somveer Keshav, Ashok Das, Sukhjit Singh, Randhir Singh, Mehakpreet Singh   +4 more
wiley   +1 more source

Generalization of adomian polynomials to functions of several variables

Computers & Mathematics with Applications, 1992
The first author developed the analytic method for approximate solution of nonlinear ordinary and partial differential equations. To use this method, the solution \(u\) of an ordinary or partial differential equation is written as \(u=\sum^ \infty_{n=0}u_ n\) and a nonlinear term assumed to be an analytic function \(f(u)\) is represented by the series \
Adomian, G., Rach, R.
openaire   +1 more source

Uncertainty Quantification of Analytical Solutions for the Nonlinear Space and Time Fractional Order ϕ4$$ {\phi}^4 $$ Equation Under Fuzziness

Engineering Reports, Volume 8, Issue 7, July 2026.
Analytical fuzzy soliton solutions of a modified space–time fractional ϕ4$$ {\phi}^4 $$ model are derived using EHFM, capturing memory effects and uncertainty. Results reveal diverse wave structures and show how fractional order and fuzziness significantly influence soliton amplitude, localization, and propagation, with heightened sensitivity near the ...
Mohsin Khalid, Neha Andaleeb Khalid, Baboucarr Ceesay, Zafar Iqbal   +3 more
wiley   +1 more source

Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods

Journal of Applied Mathematics, 2014
The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis.
Norhasimah Mahiddin, S. A. Hashim Ali
doaj   +1 more source

Analysis of fractional multi-dimensional Navier–Stokes equation

Advances in Difference Equations, 2021
In this paper, a hybrid method called variational iteration transform method has been implemented to solve fractional-order Navier–Stokes equation. Caputo operator describes fractional-order derivatives.
Yu-Ming Chu, Nehad Ali Shah, Praveen Agarwal, Jae Dong Chung   +3 more
doaj   +1 more source