A space-time spectral approximation for solving two dimensional variable-order fractional convection-diffusion equations with nonsmooth solutions

The study focuses on the numerical solutions of two-dimensional variable-order fractional convection-diffusion equations, which combine the principles of diffusion and convection to describe the movement of particles, energy, other physical quantities within a system. The numerical solution is obtained using shifted Legendre Gauss-Lobatto and shifted Chebyshev Gauss-Radau collocation techniques. The convection-diffusion equation is transformed into a system of algebraic equations utilizing shifted Chebyshev Gauss-Radau and shifted Legendre Gauss-Lobatto nodes. Additionally, numerical test examples are presented to demonstrate the method's efficacy to handle nonsmooth solutions to the given problems.