Radwan Abu-Gdairi¹, Shatha Hasan², Shrideh Al-Omari^3,*, Mohammad Al-Smadi^2,4, Shaher Momani^4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 299-313, 2022, DOI:10.32604/cmes.2022.017010 - 29 November 2021

Abstract In this paper, an efficient multi-step scheme is presented based on reproducing kernel Hilbert space (RKHS) theory for solving ordinary stiff differential systems. The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform form for a rapidly convergent series in the posed Sobolev space. Using the Gram-Schmidt orthogonality process, complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction. Consequently, by applying the standard RKHS method to each subinterval, approximate solutions that converge uniformly to the exact solutions More >

Saima Akram^1,*, Allah Nawaz¹, Muhammad Bilal Riaz², Mariam Rehman³

Intelligent Automation & Soft Computing, Vol.31, No.3, pp. 1467-1482, 2022, DOI:10.32604/iasc.2022.019767 - 09 October 2021

Abstract In this article, the maximum possible numbers of periodic solutions for the quartic differential equation are calculated. In this regard, for the first time in the literature, we developed new formulae to determine the maximum number of periodic solutions greater than eight for the quartic equation. To obtain the maximum number of periodic solutions, we used a systematic procedure of bifurcation analysis. We used computer algebra Maple 18 to solve lengthy calculations that appeared in the formulae of focal values as integrations. The newly developed formulae were applied to a variety of polynomials with algebraic More >

Ali Raza¹, Muhammad Rafiq², Dalal Alrowaili³, Nauman Ahmed⁴, Ilyas Khan^5,*, Kottakkaran Sooppy Nisar⁶, Muhammad Mohsin⁷

CMC-Computers, Materials & Continua, Vol.70, No.1, pp. 1649-1666, 2022, DOI:10.32604/cmc.2022.019148 - 07 September 2021

Abstract Nonlinear modelling has a significant role in different disciplines of sciences such as behavioral, social, physical and biological sciences. The structural properties are also needed for such types of disciplines, as dynamical consistency, positivity and boundedness are the major requirements of the models in these fields. One more thing, this type of nonlinear model has no explicit solutions. For the sake of comparison its computation will be done by using different computational techniques. Regrettably, the aforementioned structural properties have not been restored in the existing computational techniques in literature. Therefore, the construction of structural preserving… More >

V. S. Sampath Kumar^a , N. P. Pai^a,† , B. Devaki^a

Frontiers in Heat and Mass Transfer, Vol.16, pp. 1-7, 2021, DOI:10.5098/hmt.16.3

Abstract A study is carried out for the two dimensional laminar flow of conducting fluid in presence of magnetic field. The governing non-linear equations of motion are transformed in to dimensionaless form. A solution is obtained by homotopy perturbation method and it is valid for moderately large Reynolds numbers for injection at the wall. Also an efficient algorithm based finite difference scheme is developed to solve the reduced coupled ordinary differential equations with necessary boundary conditions. The effects of Reynolds number, the magnetic parameter and the pradantle number on flow velocity and tempratare distribution is analysed More >

A. A. Soliman¹, K. R. Raslan², A. M. Abdallah^3,*

Sound & Vibration, Vol.55, No.4, pp. 263-279, 2021, DOI:10.32604/sv.2021.015014 - 18 October 2021

Abstract The fundamental objective of this work is to construct a comparative study of some modified methods with Sumudu transform on fractional delay integro-differential equation. The existed solution of the equation is very accurately computed. The aforesaid methods are presented with an illustrative example. More >

Yi Yang^*, Robert A. Nawrocki, Richard M. Voyles, Haiyan H. Zhang

CMC-Computers, Materials & Continua, Vol.69, No.1, pp. 237-266, 2021, DOI:10.32604/cmc.2021.017439 - 04 June 2021

Abstract Because charge carriers of many organic semiconductors (OSCs) exhibit fractional drift diffusion (Fr-DD) transport properties, the need to develop a Fr-DD model solver becomes more apparent. However, the current research on solving the governing equations of the Fr-DD model is practically nonexistent. In this paper, an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices. The Fr-DD model is composed of two fractional-order carriers (i.e., electrons and holes) continuity equations coupled with Poisson’s equation. By treating the current density as constants within each pair… More >

Kamil Khan¹, Arshed Ali^1,*, Fazal-i-Haq², Iltaf Hussain³, Nudrat Amir⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 673-692, 2021, DOI:10.32604/cmes.2021.012730 - 21 January 2021

Abstract This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation (PIDE) with a weakly singular kernel. Cubic trigonometric B-spline (CTBS) functions are used for interpolation in both methods. The first method is CTBS based collocation method which reduces the PIDE to an algebraic tridiagonal system of linear equations. The other method is CTBS based differential quadrature method which converts the PIDE to a system of ODEs by computing spatial derivatives as weighted sum of function values. An efficient tridiagonal solver is used for the solution of the linear system… More >

Liqun Wang¹, Zengtao Chen², Guolai Yang^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 479-503, 2021, DOI:10.32604/cmes.2021.011954 - 21 January 2021

Abstract This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion (PCE). The uncertainty parameters with sufficient information are regarded as stochastic variables, whereas the interval variables are used to treat the uncertainty parameters with limited stochastic knowledge. In this method, the PCE model is constructed through the Galerkin projection method, in which the sparse grid strategy is used to generate the integral points and the corresponding integral weights. Through the sampling in PCE, the original dynamic systems with hybrid stochastic and interval parameters can be transformed into… More >

Wasfi Shatanawi^1,2,3, Ali Raza^4,5,*, Muhammad Shoaib Arif⁴, Muhammad Rafiq⁶, Mairaj Bibi⁷, Muhammad Mohsin⁸

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 201-215, 2021, DOI:10.32604/cmes.2021.012111 - 22 December 2020

Abstract Nonlinear stochastic modelling plays an important character in the different fields of sciences such as environmental, material, engineering, chemistry, physics, biomedical engineering, and many more. In the current study, we studied the computational dynamics of the stochastic dengue model with the real material of the model. Positivity, boundedness, and dynamical consistency are essential features of stochastic modelling. Our focus is to design the computational method which preserves essential features of the model. The stochastic non-standard finite difference technique is most efficient as compared to other techniques used in literature. Analysis and comparison were explored in More >

Wasfi Shatanawi^1,2,3, Ali Raza^4,5,*, Muhammad Shoaib Arif⁴, Kamaledin Abodayeh¹, Muhammad Rafiq⁶, Mairaj Bibi⁷

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1121-1137, 2021, DOI:10.32604/cmc.2020.012070 - 26 November 2020

Abstract Nonlinear stochastic modeling plays a significant role in disciplines such as psychology, finance, physical sciences, engineering, econometrics, and biological sciences. Dynamical consistency, positivity, and boundedness are fundamental properties of stochastic modeling. A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation. Well-known explicit methods such as Euler Maruyama, stochastic Euler, and stochastic Runge–Kutta are investigated for the stochastic model. Regrettably, the above essential properties are not restored by existing methods. Hence, there is a need to construct essential properties preserving the computational method. The non-standard approach of finite difference is examined More >