Results 41 to 50 of about 445 (153)

An efficient and accurate modified Adomian decomposition method for solving the Helmholtz equation with high-wavenumber [PDF]

Surveys in Mathematics and its Applications
This paper presents a modified Adomian decomposition method (MADM) for solving the one and two-dimensional Helmholtz equation with large wavenumbers. The standard Adomian decomposition method (ADM) suffers from severe divergence issues as the wavenumber ...
Saleem Nasser Alomari , Yahya Qaid Hasan   +1 more
doaj  

Solution of Time‐Fractional Coupled Burgers Equations by the Yang Transform Adomian Decomposition Method

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, the Yang transform Adomian decomposition method (YTADM) is employed in the solution of nonlinear time‐fractional coupled Burgers equations. The technique solves the fractional and nonlinear terms successfully via the Adomian decomposition of the Yang transform.
Mustafa Ahmed Ali, Mehmet Merdan, Yeou Jiann Lim   +2 more
wiley   +1 more source

Semi‐Analytical Solution of Energy and Momentum Equations With Robin′s Boundary Conditions in a Microchannel Flow

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this study, the nonlinear momentum and energy equations governing magnetohydrodynamic microchannel flow are solved under a Robin‐type slip boundary condition. To impose the mixed boundary conditions directly in the semi‐analytical construction, the Adomian decomposition method (ADM) is combined with the Fourier transform.
Ali Fooladvand, S. S. Nourazar, A. Nazari-Golshan, Masoud Rabeti, Burhan Tiryakio?lu   +4 more
wiley   +1 more source

Solving linear optimal control problems of the time-delayed systems by Adomian decomposition method [PDF]

Iranian Journal of Numerical Analysis and Optimization, 2019
We apply the Adomian decomposition method (ADM) to obtain a subop timal control for linear time-varying systems with multiple state and control delays and with quadratic cost functional.
S.M. Mirhosseini-Alizamini
doaj   +1 more source

A Reliable Decomposition Method for Fractional‐Order Fokker–Planck Equation

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This study analytically investigates the fractional Fokker–Planck equations (F‐FPEs) by employing the Sumudu decomposition method (SDM). This method combines the strengths of the Sumudu transform and the Adomian decomposition method (ADM) to effectively handle the nonlocality and memory characteristics inherent in governing fractional differential ...
Mona Alsulami, Norah Sharif Al-Yazidi, Anwarud Din   +2 more
wiley   +1 more source

Existence, Stability, and Numerical Methods for Multi-Fractional Integro-Differential Equations with Singular Kernel

Mathematics
This work investigates the solutions of fractional integro-differential equations (FIDEs) using a unique kernel operator within the Caputo framework. The problem is addressed using both analytical and numerical techniques.
Pratibha Verma, Wojciech Sumelka
doaj   +1 more source

Application of Natural Transform Method to Fractional Pantograph Delay Differential Equations

Journal of Mathematics, 2019
In this paper, a new method based on combination of the natural transform method (NTM), Adomian decomposition method (ADM), and coefficient perturbation method (CPM) which is called “perturbed decomposition natural transform method” (PDNTM) is ...
M. Valizadeh, Y. Mahmoudi, F. Dastmalchi Saei   +2 more
doaj   +1 more source

Symbolic Generation of Adomian Polynomials for Different Nonlinearities by Python [PDF]

Journal of Chemical and Petroleum Engineering
The Adomian decomposition method (ADM) is a powerful mathematical technique to find closed-form solutions to nonlinear functional equations including ODEs, PDEs, differential-difference, integral, integro-differential, algebraic, and transcendental ...
Mohsen Noorimohammad, Asadollah Houshmand, Hooman Fatoorehchi   +2 more
doaj   +1 more source

Accuracy Estimation of the Numerical Solutions for Chaotic Regime of the Pendulum With External and Parametric Excitation

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This study involves the development of a framework for checking the accuracy of built‐in algorithms from Mathcad software. The built‐in algorithms used inside Mathcad software include Runge–Kutta method of the fourth order (RK4), Adams method, backward differential formula, AdamsBDF, Radau, Bulstoer, Stiffr, and Stiffb methods.
M. C. Kekana, M. Y. Shatalov, S. E. Fadugba, N. Jeeva, T. O. Tong, Theodore Simos   +5 more
wiley   +1 more source

A Novel Computational Technique for Numerical Approximation of Nonlinear Fractional Dynamical Systems: Convergence and Efficiency Analysis

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this work, we study a family of nonlinear fractional dynamical systems and propose a numerical procedure based on the power series iterative method (PSIM). The systems are formulated in terms of the Atangana–Baleanu–Caputo (ABC) fractional derivative, which is well‐suited to the modeling of memory and nonlocal effects.
Faten H. Damag, Amin Saif, Mohammed Alsharafi, Lakhlifa Sadek   +3 more
wiley   +1 more source