A small time solutions for the KdV equation using Bubnov-Galerkin finite element method
Amein, N., Ramadan, M. (2011). A small time solutions for the KdV equation using Bubnov-Galerkin finite element method. EKB Journal Management System, 19(3), 118-125. doi: 10.1016/j.joems.2011.10.005
N. K. Amein; M. A. Ramadan. "A small time solutions for the KdV equation using Bubnov-Galerkin finite element method". EKB Journal Management System, 19, 3, 2011, 118-125. doi: 10.1016/j.joems.2011.10.005
Amein, N., Ramadan, M. (2011). 'A small time solutions for the KdV equation using Bubnov-Galerkin finite element method', EKB Journal Management System, 19(3), pp. 118-125. doi: 10.1016/j.joems.2011.10.005
Amein, N., Ramadan, M. A small time solutions for the KdV equation using Bubnov-Galerkin finite element method. EKB Journal Management System, 2011; 19(3): 118-125. doi: 10.1016/j.joems.2011.10.005

A small time solutions for the KdV equation using Bubnov-Galerkin finite element method

Journal of the Egyptian Mathematical Society
Volume 19, Issue 3, September 2011, Pages 118-125    PDF (511.67 K)
DOI: 10.1016/j.joems.2011.10.005
Authors
N. K. Amein; M. A. Ramadan
Department of Mathematics, Faculty of Science, Suez Canal University, Port Said, Egypt
Abstract
A Bubnov-Galerkin finite element method with quintic B-spline functions taken as element shape and weight functions is presented for the solution of the KdV equation. To demonstrate the accuracy, efficiency and reliability of the method three experiments are undertaken for both the evolution of a single solitary wave and the interaction of two solitary waves. The numerical results are compared with analytical solutions and the numerical results in the literature. It is shown that the method presented is accurate, efficient and can be used at small times when the analytical solution
is not known.
Keywords
KdV equation Quintic B-splines; Bubnov Galerkin method; Finite element method
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