Convergence of operator splittings for locally Lipschitz-continuous operators in Banach spaces

Ladics, Tamás

doi:10.1016/j.camwa.2015.10.015

Cited by 1 publication

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“…This resulting system is solved by operator splitting methods that are well known in problem solving that result in large systems of partial differential equations, as well as problems involving nonlinear chemical reactions [ 34 ], mosquito dispersal [ 35 ], nonlinear Schrodinger applications [ 36 ] and others. Sequential and iterative splitting for nonlinear problems with locally Lipschitz-continuous operators, which generates the lowest splitting error and convergence of first order, was presented and verified in [ 37 ]. We use the sequential operator to split the system into two parts and solve each one separately with specialized numerical techniques, in this case, combining the well-known fourth order Runge-Kutta method for the nonlinear dynamic problem and the space-time finite element method with distributed parameters for the diffusion problem.…”

Section: Introductionmentioning

confidence: 99%

Modeling the spreading and interaction between wild and transgenic mosquitoes with a random dispersal

et al. 2018

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Due to recent advances in genetic manipulation, transgenic mosquitoes may be a viable alternative to reduce some diseases. Feasibility conditions are obtained by simulating and analyzing mathematical models that describe the behavior of wild and transgenic populations living in the same geographic area. In this paper, we present a reaction–diffusion model in which the reaction term is a nonlinear function that describes the interaction between wild and transgenic mosquitoes, considering the zygosity, and the diffusive term that represents a nonuniform spatial spreading characterized by a random diffusion parameter. The resulting nonlinear system of partial differential equations is numerically solved using the sequential operator splitting technique, combining the finite element method and Runge-Kutta method. This scheme is numerically implemented considering uncertainty in the diffusion parameters of the model. Several scenarios simulating spatial release strategies of transgenic mosquitoes are analyzed, demonstrating an intrinsic association between the transgene frequency in the total population and the strategy adopted.

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