Pseudospectral method and Darvishi's preconditioning for solving system of time dependent partial differential equations

In this paper, we solve system of time dependent partial differential equations (PDEs) by using pseudospectral method and Darvishi's preconditioning. To reduce round-off error in spectral collocation method we use Darvishi's preconditioning. Firstly, theory of application of spectral collocation method on system of time dependent partial differential equations presented. This method yields a system of ordinary differential equations (ODEs). Secondly, we use fourth-order Runge-Kutta formula for the numerical integration of the system of ODE. We consider some examples to illustrate the performance of the method described.