A local meshless method for the numerical solution of multi-term time-fractional generalized Oldroyd-B fluid model.

This work presents an accurate and efficient method, for solving a two dimensional time-fractional Oldroyd-B fluid model. The proposed method couples the Laplace transform (LT) with a radial basis functions based local meshless method (LRBFM). The suggested numerical scheme first uses the LT which transform the given equation to an elliptic equation in LT space, and then it utilizes the LRBFM to solve transformed equation in LT space, and then the solution is converted back into the time domain via the improved Talbot's scheme. The local meshless methods are widely recognized for scattered data interpolation and for solving PDEs in complex shaped domains. The adaptability, simplicity, and ease of use are features that have led to the popularity of local meshless methods. The local meshless methods are easy and straightforward, they only requires to solve linear system of equations. The main objective of using the LT is to avoid the computation of costly convolution integral in time-fractional derivative and the effect of time stepping on accuracy and stability of numerical solution. The stability and the convergence of the proposed numerical scheme are discussed. Further, the Ulam-Hyers (UH) stability of the proposed model is discussed. The accuracy and efficiency of the suggested numerical approach have been demonstrated using numerical experiments on five different domains with regular nodes distribution.