Numerical evaluation of fractional Tricomi-type model arising from physical problems of gas dynamics

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The fractional Tricomi-type model is adopted for describing the anomalous process of nearly sonic speed gas dynamics.

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A new hybrid scheme based LRBF-FD method is formulated to solve the model.

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The LRBF-FD method useful for irregular domains with good accuracy is proposed.

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The stability and convergence of the proposed method are analyzed using the energy method.

This paper deals with approximating the time fractional Tricomi-type model in the sense of the Caputo derivative. The model is often adopted for describing the anomalous process of nearly sonic speed gas dynamics. The temporal semi-discretization is computed via a finite difference algorithm, while the spatial discretization is obtained using the local radial basis function in a finite difference mode. The local collocation method approximates the differential operators using a weighted sum of the function values over a local collection of nodes (named stencil) through a radial basis function expansion. This technique considers merely the discretization nodes of each subdomain around the collocation node. This leads to sparse systems and tackles the ill-conditioning produced of global collocation. The theoretical convergence and stability analyses of the proposed time semi-discrete scheme are proved by means of the discrete energy method. Numerical results confirm the accuracy and efficiency of the new approach.