The locally extrapolated exponential time differencing LOD scheme for multidimensional reaction-diffusion systems

This paper introduces the local extrapolation of first order locally one-dimensional exponential time differencing scheme for numerical solution of multidimensional nonlinear reaction-diffusion systems. This novel scheme has the benefit of solving multidimensional problems in locally one dimensional fashion by implementing sequences of tridiagonal matrix solvers instead of solving a banded system. The storage size needed for solving systems in higher dimensions with this scheme is similar to that needed for one spatial dimension systems. The stability, monotonicity, and convergence of the locally extrapolated exponential time differencing scheme have been examined. Stability analysis shows that the scheme is strongly stable (L-stable) and is particularly beneficial to nonlinear partial differential equations with irregular initial data or discontinuity involving initial and boundary conditions due to its ability to damp spurious oscillations caused by high frequency components in the solution. The performance of the novel scheme has been investigated by testing it on a two-dimensional Schnakenberg model, two and three-dimensional Brusselator models, and a three-dimensional enzyme kinetics of Michaelis-Menten type reaction-diffusion model. Numerical experiments demonstrate the efficiency, accuracy, and reliability of the scheme. (C) 2015 Elsevier B.V. All rights reserved.