Adaptive moving knots meshless method for simulating time dependent partial differential equations

This paper presents an improvement of Huang's moving knots method (Huang et al.) for solving the PDE on the contours of Equidistribution Principle (EP-contours). Firstly, a new moving knots strategy is generated by discovering a significant factor ignored (dropped) by Huang (Huang et al.). The proposed strategy ensures that arbitrary initial knots could asymptotically converge to the EP-contours. Then the moving knots strategy and PDE are simulated by using multi-quadric (MQ) quasi-interpolation step by Step (3.3, 3.4). Error estimates of the algorithm are given. At last, numerical experiments are provided to illustrate the validity of the algorithm. Both theoretical analysis and numerical results show that the proposed algorithm benefits the methods in Huang et al. and Wu.