An Efficient Local Formulation for Time–Dependent PDEs
Imtiaz Ahmad,
Muhammad Ahsan,
Zaheer-ud Din,
Ahmad Masood,
Poom Kumam
Affiliations
Imtiaz Ahmad
Department of Mathematics, University of Swabi, Swabi 23430, Pakistan
Muhammad Ahsan
Department of Mathematics, University of Swabi, Swabi 23430, Pakistan
Zaheer-ud Din
Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
Ahmad Masood
Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
Poom Kumam
KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
In this paper, a local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs. This local approach has flexibility with respect to geometry along with high order of convergence rate. In case of global meshless methods, the two major deficiencies are the computational cost and the optimum value of shape parameter. Therefore, research is currently focused towards localized RBFs approximations, as proposed here. The proposed local meshless procedure is used for spatial discretization, whereas for temporal discretization, different time integrators are employed. The proposed local meshless method is testified in terms of efficiency, accuracy and ease of implementation on regular and irregular domains.
