A hybrid LRBF-DQ method for solving nonlinear (2 + 1) dimensional initial-boundary value problems. (December 2022) - Niknam, Sepideh; Adibi, Hojatollah; Amirfakhrian, Majid
Abstract: In this paper, a combination of local radial basis functions (LRBFs) and step-by-step differential quadrature method (DQM) is proposed to solve nonlinear (2 + 1) dimensional differential equations. The LRBFs are employed to estimate spatial derivatives whereas DQM is utilized to discretize temporal derivatives. Then, the capability of the method is proved via solving five examples including Burgers', Zakharov-Kuznetsov, sine-Gordon and nonlinear chemical reaction-diffusion equations through both a rectangular and a complex domain. Furthermore, an experimental convergence analysis is conducted for each example. Moreover, the accuracy of the solution method is studied by calculating the error norms. Finally, the results are compared with those obtained in literature to prove the superiority of this scheme over particular previously proposed methods.