Results 31 to 40 of about 11,407,574 (171)

An efficient approach for the numerical solution of fifth-order KdV equations

Open Mathematics, 2020
The main aim of this article is to use a new and simple algorithm namely the modified variational iteration algorithm-II (MVIA-II) to obtain numerical solutions of different types of fifth-order Korteweg-de Vries (KdV) equations.
Ahmad Hijaz, Khan Tufail A., Yao Shao-Wen   +2 more
doaj   +1 more source

Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations

MATEC Web of Conferences, 2016
Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic) Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in
Mishra Vinod, Rani Dimple
doaj   +1 more source

A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

Mathematical Methods in the Applied Sciences, EarlyView.
A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay, Mtema James Chin, Nazim I. Mahmudov   +2 more
wiley   +1 more source

On the numerical solution of Fredholm-type integro-differential equations using an efficient modified Adomian decomposition method [PDF]

Mathematics and Computational Sciences
The efficiency of the Adomian decomposition method in the solution of integro-differential equations cannot be overemphasized. However, improvement of the method is needed as its drawbacks have been analyzed and reported in recent literature.
Kabiru Kareem, Morufu Olayiwola, Muideen Ogunniran   +2 more
doaj   +1 more source

A Unified Block‐Modal Framework for Inverse Source Problems in Heat and Mass Transfer

International Journal for Numerical Methods in Engineering, Volume 127, Issue 19, 15 October 2026.
ABSTRACT This work presents a unified block–modal framework for inverse source identification in linear diffusive problems arising in heat and mass transfer. Starting from a general parabolic model with mixed boundary operators, the Classical Integral Transform Technique is employed to project the dynamics onto an orthonormal eigenbasis, yielding a ...
André J. P. de Oliveira, Diego C. Knupp, Lucas L. S. Costa, Luiz A. S. Abreu, Mousa J. Huntul, Antônio J. Silva Neto   +5 more
wiley   +1 more source

A modified decomposition [PDF]

, 1992
The Maclaurin series is quite limited in comparison to the (Adomian) series obtained in the decomposition method. By adding procedures from the decomposition method and the expansion of nonlinearities using the Adomian polynomials, as well as a recent ...
Adomian, G., Rach, R., Meyers, R.E.
core   +1 more source

Usage of numerical methods to solve nonlinear mixed Volterra-Fredholm integral equations and their system

Results in Nonlinear Analysis, 2021
In this paper, we apply the homotopy perturbation method (HPM), modified homotopy perturbation method (MHPM), variational iteration method (VIM), Adomian decomposition method (ADM), and modified Adomian decomposition method (MADM) to solve nonlinear ...
Fawziah M. Al-saar, Kirtiwant P. Ghadle
doaj   +1 more source

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

Artificial Intelligence for Engineering, Volume 2, Issue 3, Page 251-264, September 2026.
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 decomposition method for solving initial value problems in vibration models

MATEC Web of Conferences, 2018
A number of engineering problems have second-order ordinary differential equations as their mathematical models. In practice, we may have a large scale problem with a large number of degrees of freedom, which must be solved accurately.
Mungkasi Sudi, Ekaputra I Made Wicaksana
doaj   +1 more source

Computational Investigation of MHD Radiative Flow of Shape‐Dependent Al2O3$$ A{l}_2{O}_3 $$ and Fe3O4$$ F{e}_3{O}_4 $$ Nanofluids in A Semi‐Porous Channel

Engineering Reports, Volume 8, Issue 8, August 2026.
A computational study of unsteady MHD radiative nanofluid flow in a semi‐porous channel reveals that nanoparticle shape, volume fraction, and magnetic effects significantly influence velocity and heat transfer. Results highlight strong coupling between geometric, electromagnetic, and thermophysical parameters in optimizing thermal system performance ...
Mahmmoud M. Syam, Sondos M. Syam, Muhammed I. Syam   +2 more
wiley   +1 more source