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

• Autor(a) principal: Nikan, O.
• Data de Publicação: 2020
• Outros Autores: Machado, J. A. Tenreiro, Avazzadeh, Z., Jafari, H.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.22/19004
• topic: Caputo fractional derivative; Time fractional Tricomi-type model; LRBF-FD; Stability analysis

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.