A meshless method for solving nonlinear variable-order fractional Ginzburg–Landau equations on arbitrary domains

Meshless method is an effective method to solve many kinds of equations on arbitrary domains. However, previous meshless techniques, such as moving least square method, radious basis function method, and element free Galerkin method, often have complex shape functions, which make the ill-condition of the equation increase along with the adding of control points. In order to overcome above shortcomings, in this paper, we construct a new meshless method for solving nonlinear variable order fractional Ginzburg–Landau equation. The method uses the bases of bicubic spline space as shape functions and applies continuation technique to make the operation simple and the calculation accelerated. Eventually, numerical examples demonstrate that our method can obtain higher accuracy and efficiency even though the step size is larger than other methods.