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Browsing by Author "Darvishi, Elham"

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    Article
    A geometric approach for solving the density-dependent diffusion Nagumo equation
    (Springer International Publishing, 2016) Baleanu, Dumitru; Darvishi, Elham; Baleanu, Dumitru
    In this paper, some solutions of the density-dependent diffusion Nagumo equation are obtained by using a new approach, the Lie symmetry group-preserving scheme (LSGPS). The effects of various model parameters on the solution are investigated graphically using LSGPS. Finally, a different reduction method of PDEs is applied to construct two new analytical solutions and a first integral of the Nagumo equation.
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    Article
    Solving the time-fractional diffusion equation using a lie group integrator
    (Vinca Inst Nuclear Sci, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Parto-Haghighi, Mohammad; Darvishi, Elham
    In this paper, we propose a numerical method to approximate the solutions of time fractional diffusion equation which is in the class of Lie group integrators. Our utilized method, namely fictitious time integration method transforms the unknown dependent variable to a new variable with one dimension more. Then the group preserving scheme is used to integrate the new fractional partial differential equations in the augmented space R3+1. Effectiveness and validity of method demonstrated using two examples.