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IMPLICIT-EXPLICIT METHODS FOR A CLASS OF NONLINEAR NONLOCAL GRADIENT FLOW EQUATIONS MODELLING COLLECTIVE BEHAVIOUR

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dc.creatorLUIS MIGUEL VILLADA OSORIO
dc.date2019
dc.date.accessioned2025-01-10T15:05:22Z
dc.date.available2025-01-10T15:05:22Z
dc.date.issued2019
dc.description.abstractTHE NUMERICAL SOLUTION OF NONLINEAR CONVECTION-DIFFUSION EQUATIONS WITH NONLOCAL FLUX BY EXPLICIT FINITE DIFFERENCE METHODS IS COSTLY DUE TO THE LOCAL SPATIAL CONVOLUTION WITHIN THE CONVECTIVE NUMERICAL FLUX AND THE DISADVANTAGEOUS COURANT-FRIEDRICHS-LEWY (CFL) CONDITION CAUSED BY THE DIFFUSION TERM. MORE EFFICIENT NUMERICAL METHODS ARE OBTAINED BY APPLYING SECOND-ORDER IMPLICIT-EXPLICIT (IMEX) RUNGE-KUTTA TIME DISCRETIZATIONS TO AN AVAILABLE EXPLICIT SCHEME FOR SUCH MODELS IN CARRILLO ET AL. (2015) [13]. THE RESULTING IMEX-RK METHODS REQUIRE SOLVING NONLINEAR ALGEBRAIC SYSTEMS IN EVERY TIME STEP. IT IS PROVEN, FOR A GENERAL NUMBER OF SPACE DIMENSIONS, THAT THIS METHOD IS WELL DEFINED. NUMERICAL EXPERIMENTS FOR SPATIALLY TWO-DIMENSIONAL PROBLEMS MOTIVATED BY MODELS OF COLLECTIVE BEHAVIOUR ARE CONDUCTED WITH SEVERAL ALTERNATIVE CHOICES OF THE PAIR OF RUNGE-KUTTA SCHEMES DEFINING AN IMEX-RK METHOD. FOR FINE DISCRETIZATIONS, IMEX-RK METHODS TURN OUT MORE EFFICIENT IN TERMS OF REDUCTION OF ERROR VERSUS CPU TIME THAN THE ORIGINAL EXPLICIT METHOD.
dc.formatapplication/pdf
dc.identifier.doi10.1016/j.apnum.2019.04.018
dc.identifier.issn1873-5460
dc.identifier.issn0168-9274
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/10364
dc.languagespa
dc.publisherAPPLIED NUMERICAL MATHEMATICS
dc.relation.uri10.1016/j.apnum.2019.04.018
dc.rightsPUBLICADA
dc.titleIMPLICIT-EXPLICIT METHODS FOR A CLASS OF NONLINEAR NONLOCAL GRADIENT FLOW EQUATIONS MODELLING COLLECTIVE BEHAVIOUR
dc.title.alternativeMÉTODOS IMPLÍCITO-EXPLÍCITOS PARA UNA CLASE DE ECUACIONES DE FLUJO DE GRADIENTE NO LOCAL NO LINEAL QUE MODELAN EL COMPORTAMIENTO COLECTIVO
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
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