An Efficient Discrete Model to Approximate the Solutions of a Nonlinear Double-Fractional

In this work, we present and theoretically analyze a relatively simple numerical algorithm to solve a double fraction condensate model. The mathematical system is a generalization of the famous Gross-Pitaevskii equations, which is a model consisting of two nonlinear complex-valued diffusive differential equations. The continuous model studied in this manuscript is a multidimensional system that includes Riesz-type spatial fractional derivatives. We test here the relevant features of the numerical algorithm, and illustrative simulations will be shown to verify the quadratic order of convergence in space and time variables.
[2022]

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