Some properties of a solution and finite difference scheme for one nonlinear partial differential model based on the Maxwell system. (English) Zbl 1404.65092
Summary: Linear stability and Hoph bifurcation of a solution of the initial-boundary value problem as well as the finite difference scheme for one system of nonlinear partial differential equations are investigated. The blow up case is fixed. The mentioned system is based on the Maxwell equations which describe the process of electromagnetic field penetration into a substance. Numerous computer experiments are carried out and relying on the obtained results, some graphical illustrations are presented.
MSC:
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
35B40 | Asymptotic behavior of solutions to PDEs |
35B32 | Bifurcations in context of PDEs |
35B44 | Blow-up in context of PDEs |
92C80 | Plant biology |
78A25 | Electromagnetic theory (general) |