A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation
In this research work, we proposed a Haar wavelet collocation method (HWCM) for the numerical solution of first- and second-order nonlinear hyperbolic equations. The time derivative in the governing equations is approximated by a finite difference. The nonlinear hyperbolic equation is converted into...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-05-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0203 |
| _version_ | 1797816753055596544 |
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| author | Lei Weidong Ahsan Muhammad Khan Waqas Uddin Zaheer Ahmad Masood |
| author_facet | Lei Weidong Ahsan Muhammad Khan Waqas Uddin Zaheer Ahmad Masood |
| author_sort | Lei Weidong |
| collection | DOAJ |
| description | In this research work, we proposed a Haar wavelet collocation method (HWCM) for the numerical solution of first- and second-order nonlinear hyperbolic equations. The time derivative in the governing equations is approximated by a finite difference. The nonlinear hyperbolic equation is converted into its full algebraic form once the space derivatives are replaced by the finite Haar series. Convergence analysis is performed both in space and time, where the computational results follow the theoretical statements of convergence. Many test problems with different nonlinear terms are presented to verify the accuracy, capability, and convergence of the proposed method for the first- and second-order nonlinear hyperbolic equations. |
| first_indexed | 2024-03-13T08:42:22Z |
| format | Article |
| id | doaj.art-bd497ccafe6e463baefa82532336b5df |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-03-13T08:42:22Z |
| publishDate | 2023-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-bd497ccafe6e463baefa82532336b5df2023-05-30T09:12:52ZengDe GruyterDemonstratio Mathematica2391-46612023-05-0156188990410.1515/dema-2022-0203A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equationLei Weidong0Ahsan Muhammad1Khan Waqas2Uddin Zaheer3Ahmad Masood4School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, ChinaSchool of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, ChinaDepartment of Mathematics, University of Swabi, Swabi 23430, PakistanDepartment of Basic Sciences, CECOS University of Information Technology and Emerging Sciences Peshawar, Peshawar 25000, PakistanDepartment of Basic Sciences, University of Engineering and Technology, Peshawar, PakistanIn this research work, we proposed a Haar wavelet collocation method (HWCM) for the numerical solution of first- and second-order nonlinear hyperbolic equations. The time derivative in the governing equations is approximated by a finite difference. The nonlinear hyperbolic equation is converted into its full algebraic form once the space derivatives are replaced by the finite Haar series. Convergence analysis is performed both in space and time, where the computational results follow the theoretical statements of convergence. Many test problems with different nonlinear terms are presented to verify the accuracy, capability, and convergence of the proposed method for the first- and second-order nonlinear hyperbolic equations.https://doi.org/10.1515/dema-2022-0203haar wavelethyperbolic equationcollocation methodsingle- and double-soliton wave35exx65mxx65nxx00a6965t6035-xx65h0535c08 |
| spellingShingle | Lei Weidong Ahsan Muhammad Khan Waqas Uddin Zaheer Ahmad Masood A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation Demonstratio Mathematica haar wavelet hyperbolic equation collocation method single- and double-soliton wave 35exx 65mxx 65nxx 00a69 65t60 35-xx 65h05 35c08 |
| title | A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation |
| title_full | A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation |
| title_fullStr | A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation |
| title_full_unstemmed | A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation |
| title_short | A numerical Haar wavelet-finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation |
| title_sort | numerical haar wavelet finite difference hybrid method and its convergence for nonlinear hyperbolic partial differential equation |
| topic | haar wavelet hyperbolic equation collocation method single- and double-soliton wave 35exx 65mxx 65nxx 00a69 65t60 35-xx 65h05 35c08 |
| url | https://doi.org/10.1515/dema-2022-0203 |
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