PurposeThis paper aims to directly extend the homotopy perturbation method to study the coupled Burgers equations with time‐ and space‐fractional derivatives.Design/methodology/approachThe realistic numerical solutions were obtained in a form of rapidly convergent series with easily computable components.FindingsThe figures show the effectiveness and good accuracy of the proposed method.Originality/valueThe paper obtains realistic numerical solutions in a form of rapidly convergent series with easily computable components. It shows the effectiveness and good accuracy of the proposed method.
In this study, we combined homotopy perturbation and Pade techniques for solving homogeneous and inhomogeneous two-dimensional parabolic equation. Also, we apply our combined method for coupled Burgers' equations. The numerical results demonstrate that our combined method gives the approximate solution with faster convergence rate and higher accuracy than using the classic homotopy perturbation method.
In this paper, we characterize and classify all surfaces endowed with canonical principal direction relative to a space-like and light-like, constant direction in Minkowski 3-spaces.2010 Mathematics Subject Classification. Primary 53B25, Secondary 53A35, 53C50.
In this study, we define three new type ruled surfaces obtained by using the evolution of involute-evolute curve pair in Euclidean 3-space. Then, we give some nice results for the Gaussian curvature and the mean curvature of these surfaces. Moreover, considering the given involute-evolute curve pair, the graphics of these new type surfaces were drawn with the help of Mathematica.
In this paper, we study three types of rotational surfaces in Galilean 3-spaces. We classify rotational surfaces satisfying L 1 G = F (G + C) for some constant vector C ∈ G 3 and smooth function F , where L 1 denotes the Cheng-Yau operator.
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