On Non-Isotropic Jacobi Pseudospectral Method (Journal of Computational Mathematics, 2018)
In this paper, a non-isotropic Jacobi pseudospectral method is proposed and its applications are considered. Some results on the multi-dimensional Jacobi-Gauss type interpolation and the related Bernstein-Jackson type inequalities are established, which play animportant role in pseudospectral method. The pseudospectral method is applied to a twodimensional singular problem and a problem on axisymmetric domain. The convergenceof proposed schemes is established. Numerical results demonstrate the efficiency of theproposed method.
Keywords: Jacobi pseudospectral method in multiple dimensions; Jacobi-Gauss type interpolation; Bernstein-Jackson type inequalities; Singular problem; Problem on axisymmetric domain.