An efficient numerical method for parabolic equations
Parabolic partial differential equations frequently arise in computational physics. For instance, a nonstationary heat equation and diffraction one in a paraxial approach are of this type. A system of ordinary differential
equations obtained from the initial one by discretization of the spatial Laplace operator is stiff or has rapidly oscillating parasitic solutions, so an A-stable method is to be used to solve it. All these methods include
decomposition of a huge size matrix, so can not be effective. In addition, a conventional three-node numerical formula for the Laplacian provides only second approximation order that is also not effective.
An efficient numerical method for parabolic equations is proposed and investigated. It is based on the second order Rosenbrock method for the independent coordinate with a special procedure of matrix pseudoinversion and a three-node formula with a Numerov’s corrector
for the spatial Laplacian.
CYBERNETICS AND PHYSICS, VOL. 3, No. 2, 2014, 66-72.