In the present paper explores, the Burgers' Equation which is the considerable partial differential equation that emerges in nonlinear science. Also, Homotopy Analysis Method (HAM) has been implemented to Burgers' equation with given initial conditions. The efficieny of the proposed method is analyzed by using some illustrative problems. We are compared approximate solutions acquired via HAM with the exact solutions. As a result of comparisons, it is demonstrated that the gained solutions are in excellent agreement. Additionally, 2D-3D graphs and tables of attained results are drawn by means of a ready-made package program. The recent obtained results denote that HAM is extremely efficient technique. Nonlinear partial differential equations can be solved with the help of presented method.
Abstract. In this study, we attain several spectral results for Diffusion operator. In particular, the solution functions belong to Paley-Wiener space:
In this work, one dimensional Burgers' equation and coupled Burgers' equation are solved via Homotopy perturbation method (HPM). Solutions two and three-dimensional graphics and tables of some obtained results are constructed with the help of the computational program in the Wolfram Mathematica. All the solutions found in this study validate the efficiency of the method. According to the results, we have found out that our gained solutions convergence very speedily to the analytical solutions. In conclusion, we can say that the present method can also be applied for the solutions of a wide range of nonlinear problems.
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