Iterative Operator Splitting Method For The Parabolic Equation With Variable Coefficients

We discuss in this paper solvers for heat conduction equation and convection diffusion equation with variable coefficients.We use dimension splitting method in spatial,and adopt Fourier spectral method for spatial discretization,translating into a system of ordinary differential equations.We apply iterative operator splitting scheme for the time,and using high order BDF method for temporal discretization,giving error estimation and constructing the second order and the third order iterative schemes,respectively.Numerical experiments show that the time iteration scheme can achieve second order and third order accuracy.In addition,we apply the iteration scheme and the Zassenhaus product formula to derive the weighted iteration scheme,and adopting high order Runge-Kutta method for the temporal discretization.The proposed new method can reduce the CPU time and improve accuracy than the iterative scheme.The numerical results reflected that the weighted iterative schemes can get the high accurate and high efficiency.