Results 41 to 50 of about 334 (167)
Simple parametrization methods for generating Adomian polynomials
Applicable Analysis and Discrete Mathematics, 2016 In this paper, we discuss two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions einx, where n is an integer. Some important properties of Adomian polynomials are also discussed and illustrated with examples.
KATARIA, KK, VELLAISAMY, P
openaire +4 more sources
Engineering Reports, Volume 8, Issue 2, February 2026.This paper introduces the Fractional Novel Analytical Method (FNAM), a Taylor‐series‐based technique for approximating nonlinear fractional differential‐difference equations. Built on the Caputo derivative, FNAM achieves rapid convergence without relying on Adomian polynomials, perturbation schemes, or transform methods.
Uroosa Arshad +3 more
wiley +1 more source
New Iterative Method Based on Laplace Decomposition Algorithm
Journal of Applied Mathematics, 2013 We introduce a new form of Laplace decomposition algorithm (LDA). By this form a new iterative method was achieved in which there is no need to calculate Adomian polynomials, which require so much computational time for higher-order approximations.
Sabir Widatalla, M. Z. Liu
doaj +1 more source
Advanced Theory and Simulations, Volume 9, Issue 1, January 2026.This study develops a superconvergent meshless method to analyze and control vibrations in twisted, bidirectional functionally graded Terfenol‐D beams. By optimizing magnetostrictive patch placement, it demonstrates effective vibration suppression under dynamic loads, highlighting the design potential of strategically graded materials in complex ...
Mukund A. Patil +2 more
wiley +1 more source
A Hermite Polynomial Approach for Solving the SIR Model of Epidemics
Mathematics, 2018 In this paper, the problem of the spread of a non-fatal disease in a population is solved by using the Hermite collocation method. Mathematical modeling of the problem corresponds to a three-dimensional system of nonlinear ODEs.
Aydin Secer +2 more
doaj +1 more source
A New Decomposition Method for Integro-Differential Equations
Cumhuriyet Science Journal, 2022 This present study developed a new Modified Adomian Decomposition Method (MADM) for integro-differential equations. The modification was carried out by decomposing the source term function into series.
Kabiru Kareem, Morufu Oyedunsi Olayiwola
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Kudryashov Expansion Method Applied to Fisher Mathematical Model
Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.We obtain new computational soliton solutions characterized by topological, rational, exponential, trigonometric, and hyperbolic functions for the Fisher equation. Using a good strategy, the Kudryashov expansion method is used to find different dynamical wave structures of soliton solutions within the scope of evolutionary dynamical structures of ...
Elif Deniz Öztürk +3 more
wiley +1 more source
Alexandria Engineering Journal, 2021 This article aims to introduce a new method, called the Natural Transform Iterative Method (NTIM) for the solution of fractional order differential equations. The natural transform iterative method is a modification to the natural transform decomposition
Rashid Nawaz +5 more
doaj +1 more source
Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.A numerical collocation approach employing independence polynomials of paths is formulated to approximate the solutions of high‐order linear Fredholm–Volterra integro‐differential problems under mixed conditions. The proposed approach transforms the given equation and conditions into a matrix form, leading to a linear system whose unknowns are the ...
Fatma Kaci, Kang-Jia Wang
wiley +1 more source
Alexandria Engineering Journal, 2023 In the fields of numerical analysis and applied science, approximating the roots of nonlinear equations is a fundamental and intriguing challenge. With the rapid advancement of computing power, solving nonlinear equations using numerical techniques has ...
Muhammad Saqib +3 more
doaj +1 more source