Oswaldo González-Gaxiola¹, Yakup Yildirim^2,3,4, Luminita Moraru^5,6, Anjan Biswas^7,8,9,10,*

FDMP-Fluid Dynamics & Materials Processing, Vol.21, No.9, pp. 2273-2287, 2025, DOI:10.32604/fdmp.2025.067959 - 30 September 2025

Abstract This study presents a numerical investigation of shallow water wave dynamics with particular emphasis on the role of surface tension. In the absence of surface tension, shallow water waves are primarily driven by gravity and are well described by the classical Boussinesq equation, which incorporates fourth-order dispersion. Under this framework, solitary and shock waves arise through the balance of nonlinearity and gravity-induced dispersion, producing waveforms whose propagation speed, amplitude, and width depend largely on depth and initial disturbance. The resulting dynamics are comparatively smoother, with solitary waves maintaining coherent structures and shock waves displaying gradual… More > Graphic Abstract

Oswaldo González-Gaxiola¹, Anjan Biswas^2,3,4,*, Ahmed H. Arnous⁵, Yakup Yildirim^6,7

CMES-Computer Modeling in Engineering & Sciences, Vol.142, No.3, pp. 2513-2525, 2025, DOI:10.32604/cmes.2025.062177 - 03 March 2025

Abstract Computational modeling plays a vital role in advancing our understanding and application of soliton theory. It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions. In the present study, we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity. This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures. The numerical simulation is accomplished through the application of an algorithm that integrates the classical… More >

Weijun Wang^1,*, Min Chen¹, Hui Yin¹, Yuan Li²

Energy Engineering, Vol.120, No.10, pp. 2433-2448, 2023, DOI:10.32604/ee.2023.028620 - 28 September 2023

Abstract To identify the parameters of the extended Debye model of XLPE cables, and therefore evaluate the insulation performance of the samples, the sparsity-promoting dynamic mode decomposition (SPDMD) method was introduced, as well the basics and processes of its application were explained. The amplitude vector based on polarization current was first calculated. Based on the non-zero elements of the vector, the number of branches and parameters including the coefficients and time constants of each branch of the extended Debye model were derived. Further research on parameter identification of XLPE cables at different aging stages based on… More >

Yu-Ming Chu¹, Saima Rashid^2,*, Shazia Karim³, Anam Sultan²

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1573-1611, 2023, DOI:10.32604/cmes.2023.027724 - 26 June 2023

Abstract The fractional-order Boussinesq equations (FBSQe) are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave. The fuzzy forms of analytical FBSQe solutions are first derived using the Adomian decomposition method. It also occurs on the sea floor as opposed to at the functionality. A set of dynamical partial differential equations (PDEs) in this article exemplify an unconfined aquifer flow implication. This methodology can accurately simulate climatological intrinsic waves, so the ripples are spread across a large demographic zone. The Aboodh… More >

Rania Saadeh¹, Ahmad Qazza¹, Aliaa Burqan¹, Shrideh Al-Omari^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3121-3139, 2023, DOI:10.32604/cmes.2023.026313 - 09 March 2023

Abstract This paper aims to investigate a new efficient method for solving time fractional partial differential equations. In this orientation, a reliable formable transform decomposition method has been designed and developed, which is a novel combination of the formable integral transform and the decomposition method. Basically, certain accurate solutions for time-fractional partial differential equations have been presented. The method under concern demands more simple calculations and fewer efforts compared to the existing methods. Besides, the posed formable transform decomposition method has been utilized to yield a series solution for given fractional partial differential equations. Moreover, several More >

Yuming Chu¹, Saima Rashid², Khadija Tul Kubra², Mustafa Inc^3,4,*, Zakia Hammouch⁵, M. S. Osman^6,*

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3025-3060, 2023, DOI:10.32604/cmes.2023.025470 - 09 March 2023

Abstract The analytical solution of the multi-dimensional, time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transform decomposition method is presented in this article. The aforesaid model is analyzed by employing Caputo fractional derivative. We deliberated three stimulating examples that correspond to the triple and quadruple Elzaki transform decomposition methods, respectively. The findings illustrate that the established approaches are extremely helpful in obtaining exact and approximate solutions to the problems. The exact and estimated solutions are delineated via numerical simulation. The proposed analysis indicates that the projected configuration is extremely meticulous, highly efficient, and More >

Yaya Wang¹, P. Veeresha², D. G. Prakasha³, Haci Mehmet Baskonus^4,*, Wei Gao⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.3, pp. 697-717, 2022, DOI:10.32604/cmes.2022.021865 - 03 August 2022

Abstract In this paper, the fractional natural decomposition method (FNDM) is employed to find the solution for the KunduEckhaus equation and coupled fractional differential equations describing the massive Thirring model. The massive Thirring model consists of a system of two nonlinear complex differential equations, and it plays a dynamic role in quantum field theory. The fractional derivative is considered in the Caputo sense, and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique. In order to illustrate and validate the efficiency of the future technique, we analyzed projected phenomena in More >

Mustafa Turkyilmazoglu^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.1, pp. 47-65, 2022, DOI:10.32604/cmes.2022.020781 - 18 July 2022

Abstract An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper. The standard Adomian Decomposition Method (ADM) is modified via introducing a functional term involving both a variable and a parameter. A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L² norm. Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate, more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus More >

Rashid Jan¹, Hassan Khan^2,3, Poom Kumam^4,5,*, Fairouz Tchier⁶, Rasool Shah², Haifa Bin Jebreen⁶

CMC-Computers, Materials & Continua, Vol.68, No.3, pp. 3185-3201, 2021, DOI:10.32604/cmc.2021.015252 - 06 May 2021

Abstract It is eminent that partial differential equations are extensively meaningful in physics, mathematics and engineering. Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior. In the present research, mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives. First, the Helmholtz equations are presented in Caputo’s fractional derivative. Then Natural transformation, along with the decomposition method, is used to attain the series form solutions of the suggested problems. For justification of the proposed technique, it is More >

Mustafa Turkyilmazoglu^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.1, pp. 1-22, 2021, DOI:10.32604/cmes.2021.012595 - 30 March 2021

Abstract The present paper is devoted to the convergence control and accelerating the traditional Decomposition Method of Adomian (ADM). By means of perturbing the initial or early terms of the Adomian iterates by adding a parameterized term, containing an embedded parameter, new modified ADM is constructed. The optimal value of this parameter is later determined via squared residual minimizing the error. The failure of the classical ADM is also prevented by a suitable value of the embedded parameter, particularly beneficial for the Duan–Rach modification of the ADM incorporating all the boundaries into the formulation. With the More >