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    Numerical Solution of Nonlinear Parabolic Type Equation in the Class of Generalized Functions with Degeneration
    (Amer Inst Physics, 2018) Sinsoysal, Bahaddin; Bal, Hakan; Yilmaz, Kubra
    In this paper, a method for obtaining the numerical solution of the first type initial boundary value problem for a second order degenerate parabolic equation is suggested. To this end, in accordance with the smoothness of the solution of the investigated problem, we introduce an auxiliary problem, as it has some advantages over the main problem, and is equivalent to the main problem in a definite sense. Using the introduced auxiliary problem, we write a more sensitive numerical scheme whose solution expresses all of the physical properties of the problem accurately. Moreover, using the auxiliary problem, we can write the higher order numerical schemes with respect to the time variable.