A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method
In the present paper, trigonometric B-spline DQM is applied to get the approximated solution of coupled 2D non-linear Burgers’ equation. This technique, named modified cubic trigonometric B-spline DQM, has been used to obtain accurate and effective numerical approximations of the above-mentioned par...
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| Format: | Article |
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University of Zielona Góra
2022-08-01
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| Series: | International Journal of Applied Mechanics and Engineering |
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| Online Access: | https://www.ijame-poland.com/A-Numerical-Approximation-of-2D-Coupled-Burgers-Equation-Using-Modified-Cubic-Trigonometric,166696,0,2.html |
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| author | Mamta Kapoor Varun Joshi |
| author_facet | Mamta Kapoor Varun Joshi |
| author_sort | Mamta Kapoor |
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| description | In the present paper, trigonometric B-spline DQM is applied to get the approximated solution of coupled 2D non-linear Burgers’ equation. This technique, named modified cubic trigonometric B-spline DQM, has been used to obtain accurate and effective numerical approximations of the above-mentioned partial differential equation. For checking the compatibility of results, different types of test examples are discussed. A comparison is done between L2 and L ∞ error norms with the previous, present results and with the exact solution. The resultant set of ODEs has been solved by employing the SSP RK 43 method. It is observed that the obtained results are improved compared to the previous numerical results in the literature. |
| first_indexed | 2024-03-12T16:33:21Z |
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| institution | Directory Open Access Journal |
| issn | 1734-4492 2353-9003 |
| language | English |
| last_indexed | 2024-03-12T16:33:21Z |
| publishDate | 2022-08-01 |
| publisher | University of Zielona Góra |
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| series | International Journal of Applied Mechanics and Engineering |
| spelling | doaj.art-49510437b7f745f0b6bc4ce4567cbaad2023-08-08T15:04:55ZengUniversity of Zielona GóraInternational Journal of Applied Mechanics and Engineering1734-44922353-90032022-08-012737910210.2478/ijame-2022-0037166696A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature MethodMamta Kapoor0Varun Joshi1Department of Mathematics, Lovely Professional University, Punjab, 144411, IndiaDepartment of Mathematics, Lovely Professional University, Punjab, 144411, IndiaIn the present paper, trigonometric B-spline DQM is applied to get the approximated solution of coupled 2D non-linear Burgers’ equation. This technique, named modified cubic trigonometric B-spline DQM, has been used to obtain accurate and effective numerical approximations of the above-mentioned partial differential equation. For checking the compatibility of results, different types of test examples are discussed. A comparison is done between L2 and L ∞ error norms with the previous, present results and with the exact solution. The resultant set of ODEs has been solved by employing the SSP RK 43 method. It is observed that the obtained results are improved compared to the previous numerical results in the literature.https://www.ijame-poland.com/A-Numerical-Approximation-of-2D-Coupled-Burgers-Equation-Using-Modified-Cubic-Trigonometric,166696,0,2.htmltrigonometric b-splinedifferential quadrature method (dqm)strong stability preserving runge-kutta 43 (ssp-rk43) schemel2 and l∞ error normscoupled 2d non-linear burgers’ equation |
| spellingShingle | Mamta Kapoor Varun Joshi A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method International Journal of Applied Mechanics and Engineering trigonometric b-spline differential quadrature method (dqm) strong stability preserving runge-kutta 43 (ssp-rk43) scheme l2 and l∞ error norms coupled 2d non-linear burgers’ equation |
| title | A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method |
| title_full | A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method |
| title_fullStr | A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method |
| title_full_unstemmed | A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method |
| title_short | A Numerical Approximation of 2D Coupled Burgers’ Equation Using Modified Cubic Trigonometric B-Spline Differential Quadrature Method |
| title_sort | numerical approximation of 2d coupled burgers equation using modified cubic trigonometric b spline differential quadrature method |
| topic | trigonometric b-spline differential quadrature method (dqm) strong stability preserving runge-kutta 43 (ssp-rk43) scheme l2 and l∞ error norms coupled 2d non-linear burgers’ equation |
| url | https://www.ijame-poland.com/A-Numerical-Approximation-of-2D-Coupled-Burgers-Equation-Using-Modified-Cubic-Trigonometric,166696,0,2.html |
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