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Öğe Chebyshev Wavelet Method for Numerical Solutions of Coupled Burgers' Equation(Hacettepe Univ, Fac Sci, 2019) Oruc, O.; Bulut, F.; Esen, A.This paper deals with the numerical solutions of one dimensional time dependent coupled Burgers' equation with suitable initial and boundary conditions by using Chebyshev wavelets in collaboration with a collocation method. The proposed method converts coupled Burgers' equations into system of algebraic equations by aid of the Chebyshev wavelets and their integrals which can be solved easily with a solver. Benchmarking of the proposed method with exact solution and other known methods already exist in the literature is made by three test problems. The feasibility of the proposed method is demonstrated by test problems and indicates that the proposed method gives accurate results in short cpu times. Computer simulations show that the proposed method is computationally cheap, fast and quite good even in the case of less number of collocation points.Öğe A Haar wavelet-finite difference hybrid method for the numerical solution of the modified Burgers' equation(Springer, 2015) Oruc, O.; Bulut, F.; Esen, A.In this paper, we investigate the numerical solutions of one dimensional modified Burgers' equation with the help of Haar wavelet method. In the solution process, the time derivative is discretized by finite difference, the nonlinear term is linearized by a linearization technique and the spatial discretization is made by Haar wavelets. The proposed method has been tested by three test problems. The obtained numerical results are compared with the exact ones and those already exist in the literature. Also, the calculated numerical solutions are drawn graphically. Computer simulations show that the presented method is computationally cheap, fast, reliable and quite good even in the case of small number of grid points.Öğe Numerical solution of the KdV equation by Haar wavelet method(Indian Acad Sciences, 2016) Oruc, O.; Bulut, F.; Esen, A.This paper aims to get numerical solutions of one-dimensional KdV equation by Haar wavelet method in which temporal variable is expanded by Taylor series and spatial variables are expanded with Haar wavelets. The performance of the proposed method is measured by four different problems. The obtained numerical results are compared with the exact solutions and numerical results produced by other methods in the literature. The comparison of the results indicate that the proposed method not only gives satisfactory results but also do not need large amount of CPU time. Error analysis of the proposed method is also investigated.Öğe Numerical Solutions of Fractional System of Partial Differential Equations By Haar Wavelets(Tech Science Press, 2015) Bulut, F.; Oruc, O.; Esen, A.In this paper, time fractional one dimensional coupled KdV and coupled modified KdV equations are solved numerically by Haar wavelet method. Proposed method is new in the sense that it doesn't use fractional order Haar operational matrices. In the proposed method L1 discretization formula is used for time discretization where fractional derivatives are Caputo derivative and spatial discretization is made by Haar wavelets. L-2 and L-infinity error norms for various initial and boundary conditions are used for testing accuracy of the proposed method when exact solutions are known. Numerical results which produced by the proposed method for the problems under consideration confirm the feasibility of Haar wavelet method combined with L1 discretization formula.Öğe Numerical Solutions of Regularized Long Wave Equation By Haar Wavelet Method(Springer Basel Ag, 2016) Oruc, O.; Bulut, F.; Esen, A.In this paper, we are going to investigate numerical solutions of the regularized long wave (RLW) equation by using Haar wavelet (HW), combined with finite difference method. The motion of a single solitary wave, interaction of two solitary waves, Maxwellian initial condition and wave undulation are our test problems for measuring performance of the proposed method. The results of computations are compared with exact solutions and those already published. and error norms and the numerical conservation laws are computed for discussing the accuracy and efficiency of the proposed method.Öğe SOME POSSIBLE FUZZY SOLUTIONS FOR SECOND ORDER FUZZY INITIAL VALUE PROBLEMS INVOLVING FORCING TERMS(Ministry Communications & High Technologies Republic Azerbaijan, 2014) Akin, O.; Khaniyev, T.; Oruc, O.; Turksen, I. B.In this paper, we state a fuzzy initial value problem of the second order fuzzy differential equations. Here, we investigate problems with fuzzy coefficients, fuzzy initial values, and fuzzy forcing functions where fuzzy terms are fuzzy numbers. We have extended the algorithm given in [2]. Finally, we present some examples by using our extended algorithm.Öğe A unified approach for the numerical solution of time fractional Burgers' type equations(Springer Heidelberg, 2016) Esen, A.; Bulut, F.; Oruc, O.In this paper, a relatively new approach is devised for obtaining approximate solution of time fractional partial differential equations. Time fractional diffusion equation and time fractional Burgers-Fisher equation are solved with Haar wavelet method where fractional derivatives are Caputo derivative. Time discretization of the problems made by L1 discretization formula and space derivatives discretized by Haar series. L-2 and L-infinity error norms are used for measuring accuracy of the proposed method. Numerical results obtained with proposed method compared with exact solutions as well as with available results from the literature. The numerical results verify the feasibility of Haar wavelet combined with L1 discretization formula for the considered problems.
