Mohammad Tamsir , Mutum Zico Meetei , Neeraj Dhiman
{"title":"通过基于立方统一和扩展三角 B-样条函数的新 DQM 对正弦-戈登方程进行数值处理","authors":"Mohammad Tamsir , Mutum Zico Meetei , Neeraj Dhiman","doi":"10.1016/j.wavemoti.2024.103409","DOIUrl":null,"url":null,"abstract":"<div><p>The purpose of this work is to propose a new composite scheme based on differential quadrature method (DQM) and modified cubic unified and extended trigonometric B-spline (CUETB-spline) functions to numerically approximate one-dimensional (1D) and two-dimensional (2D) Sine-Gordon Eqs. (SGEs). These functions are modified and then applied in DQM to determine the weighting coefficients (WCs) of spatial derivatives. Using the WCs in SGEs, we obtain systems of ordinary differential equations (ODEs) which is resolved by the five-stage and order four strong stability-preserving time-stepping Runge–Kutta (SSP-RK<sub>5,4</sub>) scheme. This method's precision and consistency are validated through numerical approximations of the one-and two-dimensional problems, showing that the projected method outcomes are more accurate than existing ones as well as an incomparable agreement with the exact solutions is found. Besides, the rate of convergence (ROC) is performed numerically, which shows that the method is second-order convergent with respect to the space variable. The proposed method is straightforward and can effectively handle diverse problems. Dev-C++ 6.3 version is used for all calculations while Figs. are drawn by MATLAB 2015b.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103409"},"PeriodicalIF":2.1000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Numerical treatment of the Sine-Gordon equations via a new DQM based on cubic unified and extended trigonometric B-spline functions\",\"authors\":\"Mohammad Tamsir , Mutum Zico Meetei , Neeraj Dhiman\",\"doi\":\"10.1016/j.wavemoti.2024.103409\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The purpose of this work is to propose a new composite scheme based on differential quadrature method (DQM) and modified cubic unified and extended trigonometric B-spline (CUETB-spline) functions to numerically approximate one-dimensional (1D) and two-dimensional (2D) Sine-Gordon Eqs. (SGEs). These functions are modified and then applied in DQM to determine the weighting coefficients (WCs) of spatial derivatives. Using the WCs in SGEs, we obtain systems of ordinary differential equations (ODEs) which is resolved by the five-stage and order four strong stability-preserving time-stepping Runge–Kutta (SSP-RK<sub>5,4</sub>) scheme. This method's precision and consistency are validated through numerical approximations of the one-and two-dimensional problems, showing that the projected method outcomes are more accurate than existing ones as well as an incomparable agreement with the exact solutions is found. Besides, the rate of convergence (ROC) is performed numerically, which shows that the method is second-order convergent with respect to the space variable. The proposed method is straightforward and can effectively handle diverse problems. Dev-C++ 6.3 version is used for all calculations while Figs. are drawn by MATLAB 2015b.</p></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"131 \",\"pages\":\"Article 103409\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Wave Motion\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165212524001392\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165212524001392","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
Numerical treatment of the Sine-Gordon equations via a new DQM based on cubic unified and extended trigonometric B-spline functions
The purpose of this work is to propose a new composite scheme based on differential quadrature method (DQM) and modified cubic unified and extended trigonometric B-spline (CUETB-spline) functions to numerically approximate one-dimensional (1D) and two-dimensional (2D) Sine-Gordon Eqs. (SGEs). These functions are modified and then applied in DQM to determine the weighting coefficients (WCs) of spatial derivatives. Using the WCs in SGEs, we obtain systems of ordinary differential equations (ODEs) which is resolved by the five-stage and order four strong stability-preserving time-stepping Runge–Kutta (SSP-RK5,4) scheme. This method's precision and consistency are validated through numerical approximations of the one-and two-dimensional problems, showing that the projected method outcomes are more accurate than existing ones as well as an incomparable agreement with the exact solutions is found. Besides, the rate of convergence (ROC) is performed numerically, which shows that the method is second-order convergent with respect to the space variable. The proposed method is straightforward and can effectively handle diverse problems. Dev-C++ 6.3 version is used for all calculations while Figs. are drawn by MATLAB 2015b.
期刊介绍:
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.