Application of efficient hybrid local meshless method for the numerical simulation of time-fractional PDEs arising in mathematical physics and finance

The article describes the implementation of an efficient hybrid local meshless technique for the numerical solution of a multi-term time-fractional mobile-immobile diffusion equation in the sense of Caputo derivative, which models an anomalous mobile-immobile solute transport process. The proposed meshless technique, based on the inverse multiquadric-cubic radial basis function, is used to discretize the space derivatives of the model, while for time derivatives, an implicit time integration is utilized. The recommended technique approximates the solution on a set of scattered/uniform nodes, leading to a sparse and well-conditioned coefficient matrix. The article focuses on the benefits of meshless techniques, emphasizing their meshless nature and ease of use in higher dimensions. The proposed technique’s numerical results are compared with analytical solutions for various test problems on both rectangular and non-rectangular computational domains. These comparisons demonstrate the successful applications and accuracy of the local meshless technique.