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Öğe A Galerkin finite element approach to Burgers' equation(2004) Dogan A.A Galerkin finite element method is presented for the numerical solution of Burgers' equation. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found via a Crank-Nicolson approach involving a product approximation. It is shown that this method is capable of solving Burgers' equation accurately for a wide range of viscosity values. The results show that the new method performs better than the most of the methods available in the literature. © 2003 Elsevier Inc. All rights reserved.Öğe Application of Galerkin's method to equal width wave equation(2005) Dogan A.The non-linear equal width equation is solved by Galerkin's method using linear finite elements. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found employing the Crank-Nicolson approach including a product approximation. The three invariants of the motion are calculated to determine the conservation properties of the system. L2 and L? error norms are used to measure differences between the exact and numerical solutions. The simulations of solitary wave motion are used to determine the properties of the algorithm. Finally, the development of an undular bore is studied. © 2003 Elsevier Inc. All rights reserved.Öğe B-spline collocation methods for numerical solutions of the RLW equation(2003) Dag I.; Dogan A.; Saka B.The numerical solution of the RLW equation is obtained by using a splitting up technique and both quadratic and cubic B-splines. Both quadratic and cubic B-spline collocation methods are applied to the resulting equation. Solutions without splitting the RLW equation are also obtained with the method of the cubic collocation method. Results are substantiated by studying propagation of a solitary wave and undular bore development. Comparison is made with results of the proposed schemes.Öğe Numerical solution of regularized long wave equation using Petrov-Galerkin method(2001) Dogan A.The regularized long wave (RLW) equation is solved by a Petrov-Galerkin method using quadratic B-spline finite elements. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is obtained via a Crank-Nicolson approach involving a product approximation. The motion of solitary waves is studied to assess the properties of the algorithm. The development of an undular bore is modelled. Copyright © 2001 John Wiley & Sons, Ltd.Öğe Numerical solution of RLW equation using linear finite elements within Galerkin's method(2002) Dogan A.The regularised long wave equation is solved by Galerkin's method using linear space finite elements. In the simulations of the migration of a single solitary wave, this algorithm is shown to have good accuracy for small amplitude waves. Moreover, for very small amplitude waves (? 0.09) it has higher accuracy than an approach using quadratic B-spline finite elements within Galerkin's method. The interaction of two solitary waves is modelled for small amplitude waves. © 2002 Elsevier Science Inc. All rights reserved.
