TY - JOUR
T1 - A Monotone Compact Implicit Scheme for Nonlinear Reaction-Diffusion Equations
JO - Journal of Computational Mathematics
VL - 2
SP - 123
EP - 148
PY - 2008
DA - 2008/04
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8616.html
KW - Nonlinear reaction-diffusion equation, Monotone compact implicit scheme,
High accuracy, Monotone iteration, Rapid convergence rate.
AB - <p style="text-align: justify;">A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate of the iteration.</p>