An efficient exponential time differencing method for nonlinear reaction diffusion problems.

摘要

A new fully discrete Exponential Time Differencing Runge-Kutta scheme for inhomogeneous parabolic partial differential equations is developed. In space we utilize the diagonal Pade scheme R1,1( z) as second order approximation to the exponential function e-z. For non-smooth initial data we use two to four steps of a lower order scheme as damping device. We prove second order convergence and show numerical experiments for a wide variety of examples supporting this result. Additionally, we apply it to a system of three partial differential equations modeling bacterial growth and to pricing of financial options in the presence of transaction costs with non-smooth payoffs.