A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements
Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standa...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/527467 |
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| author | A. A. Soliman |
| author_facet | A. A. Soliman |
| author_sort | A. A. Soliman |
| collection | DOAJ |
| description | Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable. |
| format | Article |
| id | doaj-art-8cc1fbe61a8c4734ac734f5d641bb475 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8cc1fbe61a8c4734ac734f5d641bb4752025-02-03T06:13:26ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/527467527467A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite ElementsA. A. Soliman0Department of Mathematics, Faculty of Education, Suez Canal University, Al-Arish 45111, EgyptNumerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable.http://dx.doi.org/10.1155/2012/527467 |
| spellingShingle | A. A. Soliman A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements Abstract and Applied Analysis |
| title | A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements |
| title_full | A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements |
| title_fullStr | A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements |
| title_full_unstemmed | A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements |
| title_short | A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements |
| title_sort | galerkin solution for burgers equation using cubic b spline finite elements |
| url | http://dx.doi.org/10.1155/2012/527467 |
| work_keys_str_mv | AT aasoliman agalerkinsolutionforburgersequationusingcubicbsplinefiniteelements AT aasoliman galerkinsolutionforburgersequationusingcubicbsplinefiniteelements |