Abstract
In this work, bases on the reproducing kernel theory and collocation
method, we study the space Riesz fractional Navier-Stokes equations, and
propose the numerical method to solve it. Firstly the new base space can
be constructed by the spline and reproducing kernel space. The
ε-approximate solution in binary spline space in the form of
finite terms can be derived. Through using the collocation method, the
approximate problem is solved. In addition, we provide analysis of the
stability and convergence. In final, two numerical examples are provided
to show the effectiveness of our method.