Yazar "Ucar, Y." seçeneğine göre listele
Listeleniyor 1 - 8 / 8
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe A B-spline collocation method for solving fractional diffusion and fractional diffusion-wave equations(Tbilisi Centre Math Sci, 2015) Esen, A.; Tasbozan, O.; Ucar, Y.; Yagmurlu, N. M.In this paper,we have considered the fractional diffusion and fractional diffusion wave equations in which the time derivative is a fractional derivative in the Caputo form and have obtained their numerical solutions by collocation method using cubic B-spline base functions. In the solution process, for the fractional diffusion equation L1 discretizaton formula of the fractional derivative is applied, and for the fractional diffusion-wave equation L2 discretizaton formula of the fractional derivative is applied. Accuracy of the proposed method is discussed by computing the error norms L2 and L-infinity. A stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.Öğe A new approach on numerical solutions of the Improved Boussinesq type equation using quadratic B-spline Galerkin finite element method(Elsevier Science Inc, 2015) Ucar, Y.; Karaagac, B.; Esen, A.In the present manuscript, some numerical solutions of an Improved Boussinesq type equation are obtained by means of quadratic B-spline Galerkin finite element method. Then, error norms L-2 and L-infinity have been calculated to test the accuracy of the current method. In the manuscript, solitary wave movement and interaction of solitary-antisolitary waves are considered as test problems. (C) 2015 Elsevier Inc. All rights reserved.Öğe A Numerical Approach to the Rosenau-KdV equation using Galerkin Cubic Finite Element Method(Centre Environment Social & Economic Research Publ-Ceser, 2017) Ucar, Y.; Karaagac, B.; Kutluay, S.In this paper, a Galerkin finite element method has been used to solve numerically the Rosenau-KdV equation using cubic B-spline functions. The system of ordinary differential equations obtained in terms of element parameters by the application of the method has been solved by using the fourth order Runge-Kutta method. The error norms L-2 and L-infinity together with invariants I-1 and I-2 have been calculated to show the accuracy and efficiency of the method. The computed results have been compared with exact values and also other numerical results available in the literature.Öğe Numerical solution of a coupled modified Korteweg-de Vries equation by the Galerkin method using quadratic B-splines(Taylor & Francis Ltd, 2013) Kutluay, S.; Ucar, Y.In this paper, numerical solutions of a coupled modified Korteweg-de Vries equation have been obtained by the quadratic B-spline Galerkin finite element method. The accuracy of the method has been demonstrated by five test problems. The obtained numerical results are found to be in good agreement with the exact solutions. A Fourier stability analysis of the method is also investigated.Öğe A Numerical Solution to Fractional Diffusion Equation for Force-Free Case(Hindawi Ltd, 2013) Tasbozan, O.; Esen, A.; Yagmurlu, N. M.; Ucar, Y.A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made.Öğe Numerical solutions of the coupled Burgers' equation by the Galerkin quadratic B-spline finite element method(Wiley, 2013) Kutluay, S.; Ucar, Y.In this paper, a coupled Burgers' equation has been numerically solved by a Galerkin quadratic B-spline FEM. The performance of the method has been examined on three test problems. Results obtained by the method have been compared with known exact solution and other numerical results in the literature. A Fourier stability analysis of the method is also investigated. Copyright (c) 2013 John Wiley & Sons, Ltd.Öğe Numerical Solutions of the Modified Burgers' Equation by Finite Difference Methods(De Gruyter Poland Sp Zoo, 2017) Ucar, Y.; Yagmurlu, N. M.; Tasbozan, O.In this study, a numerical solution of the modified Burgers' equation is obtained by the finite difference methods. For the solution process, two linearization techniques have been applied to get over the non-linear term existing in the equation. Then, some comparisons have been made between the obtained results and those available in the literature. Furthermore, the error norms L-2 and L-infinity are computed and found to be sufficiently small and compatible with others in the literature. The stability analysis of the linearized finite difference equations obtained by two different linearization techniques has been separately conducted via Fourier stability analysis method.Öğe SOLVING FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS BY PETROV-GALERKIN FINITE ELEMENT METHOD(Turkic World Mathematical Soc, 2014) Esen, A.; Ucar, Y.; Yagmurlu, M.; Tasbozan, O.In the last few years, it has become highly evident that fractional calculus has been widely used in several areas of science. Because of this fact, their numerical solutions also have become urgently important. In this manuscript, numerical solutions of both the fractional diffusion and fractional diffusion-wave equations have been obtained by a Petrov-Galerkin finite element method using quadratic B-spline base functions as trial functions and linear B-spline base functions as the test functions. In those equations, fractional derivatives are used in terms of the Caputo sense. While the L1 discretizaton formula has been applied to fractional diffusion equation, the L2 discretizaton formula has been applied to the fractional diffusion-wave equation. Finally, the error norms L-2 and L-infinity have been calculated for testing the accuracy of the proposed scheme.
