عنوان مجله
|
Iranian Journal of Numerical Analysis and Optimization
|
چکیده
|
In this paper, some monotonicity-preserving (MP) and positivity-preserving
(PP) splitting methods for solving the balance laws of the reaction and
diffusion source terms are investigated. To capture the solution with highaccuracy and resolution, the original equation with reaction source term
is separated through the splitting method into two sub-problems including
the homogeneous conservation law and a simple ordinary differential equation (ODE). The resulting splitting methods preserve monotonicity and
positivity property for a normal CFL condition. A trenchant numerical
analysis made it clear that the computing time of the proposed methods
decreases when the so-called MP process for the homogeneous conservation law is imposed. Moreover, the proposed methods are successful in
recapturing the solution of the problem with high-resolution in the case
of both smooth and non-smooth initial profiles. To show the efficiency of
proposed methods and to verify the order of convergence and capability of
these methods, several numerical experiments are performed through some
prototype examples.
|