Numerical study of integer-order hyperbolic telegraph model arising in physical and related sciences

Published on Sep 1, 2020in European Physical Journal Plus3.911
路 DOI :10.1140/EPJP/S13360-020-00784-Z
M. Abdel-Aty1
Estimated H-index: 1
(Sohag University)
Source
Abstract
More recently, it is discovered in the field of applied sciences and engineering that the telegraph equation is better suited to model reaction-diffusion than the ordinary diffusion equation. In this article, the second-order hyperbolic telegraph equations are analyzed numerically by means of an efficient local differential quadrature method utilizing the radial basis functions. The explicit time integration technique is used to semi-discretize the model in the time direction, while the space derivatives are discretized by the proposed meshless procedure. To test the accuracy and capabilities of the method, five test problems are considered utilizing both rectangular and non-rectangular domains, which show that the proposed scheme solutions are converging extremely quick in comparison with the different existing numerical techniques in the recent literature.
馃摉 Papers frequently viewed together
2020
References53
Newest
#1Imtiaz AhmadH-Index: 14
#2Hijaz AhmadH-Index: 24
Last. Clemente CesaranoH-Index: 21
view all 5 authors...
Fractional differential equations depict nature sufficiently in light of the symmetry properties which describe biological and physical processes. This article is concerned with the numerical treatment of three-term time fractional-order multi-dimensional diffusion equations by using an efficient local meshless method. The space derivative of the models is discretized by the proposed meshless procedure based on the multiquadric radial basis function though the time-fractional part is discretized...
Source
#1Imtiaz AhmadH-Index: 14
#2Muhammad Nawaz Khan (University of Engineering and Technology, Peshawar)H-Index: 6
Last. Kottakkaran Sooppy Nisar (Salman bin Abdulaziz University)H-Index: 31
view all 4 authors...
Abstract In this article, an efficient local meshless technique is implemented for the numerical solution of an anomalous mobile-immobile solute transport process. The process is mathematically modeled as a time fractional mobile-immobile diffusion equation in sense of Caputo derivative. An implicit time integration procedure is used to semi-discretize the model in the time direction whereas the space derivatives of the model is discretized by the proposed meshless technique based on inverse mul...
Source
#1R. Cavoretto (UNITO: University of Turin)H-Index: 4
#2A. De Rossi (UNITO: University of Turin)H-Index: 10
Abstract In this paper we present a new adaptive two-stage algorithm for solving elliptic partial differential equations via a radial basis function collocation method. Our adaptive meshless scheme is based at first on the use of a leave-one-out cross validation technique, and then on a residual subsampling method. Each of phases is characterized by different error indicators and refinement strategies. The combination of these computational approaches allows us to detect the areas that need to b...
Source
#1Yunxu Zhou (Qingdao University)H-Index: 1
#2Wenzhen Qu (Qingdao University)H-Index: 17
Last. Hongwei Gao (Qingdao University)H-Index: 8
view all 4 authors...
Abstract A hybrid meshless method is constructed in this paper for the solution of the second order hyperbolic telegraph equation in two space dimensions with Dirichlet or mixed boundary conditions. The temporal derivatives of the physical quantity included in the telegraph equation are approximated into the finite difference formulae by using the Houbolt method. Based on these formulae, the original telegraph problem is then transformed into the modified Helmholtz equation which is efficiently ...
Source
#1Roberto Cavoretto (UNITO: University of Turin)H-Index: 18
#2Alessandra De Rossi (UNITO: University of Turin)H-Index: 14
Abstract In this paper we enhance the adaptive scheme presented in Cavoretto and De Rossi (2019) for solving elliptic boundary value problems via RBF collocation methods. More precisely, this study concerns a leave one out cross validation technique applied as an error estimate and used in the adaptive refinement process. The modified algorithm we propose here allows us to get numerical convergence also when L-shape or irregular domains are considered. Moreover, a comparison between unsymmetric ...
Source
#1Muhammad Nawaz Khan (University of Engineering and Technology, Peshawar)H-Index: 6
#2Imtiaz AhmadH-Index: 14
Last. Hijaz Ahmad (University of Engineering and Technology, Peshawar)H-Index: 24
view all 3 authors...
In this study, a radial basis function collocation method (RBFCM) is proposed for the numerical treatment of inverse space-wise dependent heat source problems. Multiquadric radial basis function is applied for spatial discretization whereas for temporal discretization Runge-Kutta method of order four is employed. Numerical experiments for one, two and three dimensional cases are included to test the efficiency and accuracy of the suggested method. Both non-rectangular and rectangular geometries ...
Source
#1Hijaz Ahmad (University of Engineering and Technology, Peshawar)H-Index: 24
#2Aly R. Seadawy (Taibah University)H-Index: 66
Last. Phatiphat Thounthong (King Mongkut's University of Technology North Bangkok)H-Index: 32
view all 4 authors...
In this paper, modified variational iteration algorithm-II is investigated for finding approximate solutions of nonlinear Parabolic equations. Comparisons of the MVIA-II with trigonometric B-spline...
Source
#1Sergiy Yu. Reutskiy (NASU: National Academy of Sciences of Ukraine)H-Index: 9
#2Yuhui Zhang (Hohai University)H-Index: 5
Last. HongGuang Sun (Hohai University)H-Index: 29
view all 4 authors...
Abstract In this work, a cubic B-spline method based on finite difference and meshless approaches for solving 2D generalized telegraph equations in irregular single and multi-connected domains is presented. The three-layer Crank-Nicolson time-stepping scheme is applied for temporal derivatives and systems of second order elliptic partial differential equations (EPDEs) of general type with mixed derivatives and variable coefficients are obtained. The Dirichlet and Robin boundary conditions are co...
Source
#1Imtiaz AhmadH-Index: 14
#2Siraj-ul-IslamH-Index: 25
Last. Sakhi ZamanH-Index: 7
view all 4 authors...
This paper is concerned with the numerical solution of time- fractional partial differential equations (PDEs) via local meshless differential quadrature collocation method (LMM) using radial basis functions (RBFs). For the sake of comparison, global version of the meshless method is also considered. The meshless methods do not need mesh and approximate solution on scattered and uniform nodes in the domain. The local and global meshless procedures are used for spatial discretization. Caputo deriv...
Source
#2Hijaz AhmadH-Index: 24
Last. Nawaz Muhammad KhanH-Index: 1
view all 5 authors...
In this article, we present an efficient local meshless method for the numerical treatment of three-dimensional convection-diffusion PDEs. The demand of meshless techniques increment because of its meshless nature and simplicity of usage in higher dimensions. This technique approximates the solution on set of uniform and scattered nodes. The space derivatives of the models are discretized by the proposed meshless procedure though the time fractional part is discretized by Liouville-Caputo fracti...
Cited By11
Newest
#3Hijaz Ahmad (University of Engineering and Technology, Peshawar)H-Index: 24
#4M. D. AlsulamiH-Index: 2
Last. Taher A. Nofal (Taif University)H-Index: 12
view all 7 authors...
Abstract null null The applications of fractional partial differential equations (PDEs) in diverse disciplines of science and technology have caught the attention of many researchers. This article concerned with the approximate numerical solutions of three-dimensional two- and three-term time fractional PDE models utilizing an accurate, and computationally attractive local meshless technique. Due to their tremendous advantages like ease of applicability in higher dimensions in both regular and i...
Source
#1Imtiaz AhmadH-Index: 14
#2Hijaz Ahmad (University of Engineering and Technology, Peshawar)H-Index: 24
Last. Adil Jhangeer (Namal College)H-Index: 12
view all 7 authors...
Abstract null null This paper deals with the numerical solution utilizing local version of the meshless collocation method for time-fraction Korteweg de Vries, Burgers鈥 and Korteweg de Vries-Burgers鈥 equations. This technique generates sparse and well-conditioned coefficient matrices when applied on a set of uniform or scattered nodes. To check the accuracy of the proposed local meshless technique three test problems are solved numerically.
Source
#4M. D. AlsulamiH-Index: 2
#5Phatiphat Thounthong (King Mongkut's University of Technology North Bangkok)H-Index: 32
Fractional partial differential equation models are frequently used to several physical phenomena. Despite the ability to express many complex phenomena in different disciplines, researchers have found that multiterm time-fractional PDEs improve the modeling accuracy for describing diffusion processes in contrast to the results of a single term. Nowadays, it attracts the attention of the active researchers. The aim of this work is concerned with the approximate numerical solutions of the three-t...
Source
#2Imtiaz AhmadH-Index: 14
Last. Phatiphat Thounthong (King Mongkut's University of Technology North Bangkok)H-Index: 32
view all 5 authors...
This article provides numerical simulations of the time-fractional coupled Korteweg鈥揹e Vries and Klein鈥揋ordon equations via the local meshless collocation method (LMCM) utilising the radial basis functions. The recommended local meshless technique is utilised for the space derivatives of the models whereas Caputo fractional definition is used for time-fractional derivative. Numerical experiments are performed for one-dimensional coupled Korteweg鈥揹e Vries and two-dimensional Klein鈥揋ordon equation...
Source
#1Alamgeer KhanH-Index: 2
#2M. FarooqH-Index: 6
Last. Yu-Ming ChuH-Index: 28
view all 7 authors...
Source
#1Umair AliH-Index: 9
Source
#1Lanxin ChenH-Index: 1
#3Junxian ZhangH-Index: 1
Last. Lishuang PanH-Index: 1
view all 6 authors...
Source
#1Fuzhang Wang (Nanchang Institute of Technology)H-Index: 2
#2Enran Hou (Huaibei Normal University)H-Index: 1
In this paper, a direct meshless method (DMM), which is based on the radial basis function, is developed to the numerical solution of the two-dimensional second-order hyperbolic telegraph equations. Since these hyperbolic telegraph equations are time dependent, we present two schemes for the basis functions from radial and nonradial aspects. The first scheme is fulfilled by considering time variable as normal space variable to construct an 鈥渋sotropic鈥 space-time radial basis function. The other ...
Source
#1Shyam Sundar Santra (JIS College of Engineering)H-Index: 14
#2Omar Bazighifan (Hadramout University of Science and Technology)H-Index: 20
Last. Yu-Ming ChuH-Index: 28
view all 4 authors...
Source
#1Mehnaz Shakeel (University of Engineering and Technology, Peshawar)H-Index: 1
#2Iltaf Hussain (University of Engineering and Technology, Peshawar)H-Index: 7
Last. Ying-Fang ZhangH-Index: 2
view all 6 authors...
In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and complex geometries. Time derivative is approximated by Caputo derivative for the values of and . Forward difference scheme is applied to approximate the 1st order derivative appearing in the definition of Caputo derivative for , whereas central ...
Source
This website uses cookies.
We use cookies to improve your online experience. By continuing to use our website we assume you agree to the placement of these cookies.
To learn more, you can find in our Privacy Policy.