{"title":"A Rothe-Chebyshev collocation algorithm for the hyperbolic telegraphic type equations with variable coefficients","authors":"Mohammad Izadi , Samad Noeiaghdam , H.M. Ahmed","doi":"10.1016/j.asej.2025.103720","DOIUrl":null,"url":null,"abstract":"<div><div>We construct a semi-discretized spectral approach for the second-order telegraphic-type equations with Dirichlet or Neumann boundary conditions. The successive method of Rothe is first employed for the temporal discretization procedure to transform the model equations into a system of boundary value problems. Subsequently, the spectral matrix procedure utilizing the shifted modified Chebyshev polynomials (SMCPs) is formulated for the spatial variable. The family of discrete solutions obtained by the hybrid Rothe-SMCPs algorithm is demonstrated to exhibit uniform convergence to the continuous solution of order <span><math><mi>O</mi><mrow><mo>(</mo><mi>Δ</mi><mi>τ</mi><mo>+</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>)</mo></mrow></math></span>. In this context, Δ<em>τ</em> signifies the time step, while <em>R</em> represents the number of SMCPs employed in the approximation procedure. Simulation experiments are carried out to highlight the strong agreement between the numerical results and theoretical predictions. The numerical results utilizing a larger time-step size exhibit greater accuracy compared to the computational values available in existing research works.</div></div>","PeriodicalId":48648,"journal":{"name":"Ain Shams Engineering Journal","volume":"16 11","pages":"Article 103720"},"PeriodicalIF":5.9000,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ain Shams Engineering Journal","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2090447925004617","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We construct a semi-discretized spectral approach for the second-order telegraphic-type equations with Dirichlet or Neumann boundary conditions. The successive method of Rothe is first employed for the temporal discretization procedure to transform the model equations into a system of boundary value problems. Subsequently, the spectral matrix procedure utilizing the shifted modified Chebyshev polynomials (SMCPs) is formulated for the spatial variable. The family of discrete solutions obtained by the hybrid Rothe-SMCPs algorithm is demonstrated to exhibit uniform convergence to the continuous solution of order . In this context, Δτ signifies the time step, while R represents the number of SMCPs employed in the approximation procedure. Simulation experiments are carried out to highlight the strong agreement between the numerical results and theoretical predictions. The numerical results utilizing a larger time-step size exhibit greater accuracy compared to the computational values available in existing research works.
期刊介绍:
in Shams Engineering Journal is an international journal devoted to publication of peer reviewed original high-quality research papers and review papers in both traditional topics and those of emerging science and technology. Areas of both theoretical and fundamental interest as well as those concerning industrial applications, emerging instrumental techniques and those which have some practical application to an aspect of human endeavor, such as the preservation of the environment, health, waste disposal are welcome. The overall focus is on original and rigorous scientific research results which have generic significance.
Ain Shams Engineering Journal focuses upon aspects of mechanical engineering, electrical engineering, civil engineering, chemical engineering, petroleum engineering, environmental engineering, architectural and urban planning engineering. Papers in which knowledge from other disciplines is integrated with engineering are especially welcome like nanotechnology, material sciences, and computational methods as well as applied basic sciences: engineering mathematics, physics and chemistry.