Variable step length algorithms with high-order extrapolated non-standard finite difference schemes for a SEIR model

摘要

In the present manuscript, higher-order methods are derived to solve a SEIR model for malware propagation. They are obtained using extrapolation techniques combined with nonstandard finite difference (NSFD) schemes used in Jansen and Twizell (2002). Thus, the new algorithms are more efficient computationally, and are dynamically consistent with the continuous model. Later, different procedures are considered to control the error in the discrete schemes. Numerical experiments are provided to illustrate the theory, and for the comparison of the different strategies in the adaptation of the variable step length.