An asymptotic expansion of the global discretization error of difference schemes for numerically solving a quasilinear parabolic system of differential equations

Computing ◽  
1992 ◽  
Vol 47 (3-4) ◽  
pp. 295-308
Author(s):  
M. Meister
Keyword(s):  
Asymptotic Expansion ◽  
Differential Equations ◽  
Parabolic System ◽  
Discretization Error ◽  
Difference Schemes ◽  
System Of Differential Equations ◽  
Quasilinear Parabolic System ◽  
Quasilinear Parabolic

scholarly journals Implicit difference schemes for quasilinear parabolic functional equations

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Milena Matusik
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Difference Schemes ◽  
New Class ◽  
Implicit Difference Schemes ◽  
Functional Differential ◽  
The Stability ◽  
Quasilinear Parabolic

AbstractWe present a new class of numerical methods for quasilinear parabolic functional differential equations with initial boundary conditions of the Robin type. The numerical methods are difference schemes which are implicit with respect to time variable. We give a complete convergence analysis for the methods and we show that the new methods are considerable better than the explicit schemes. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given functions with respect to functional variables. Results obtained in the paper can be applied to differential equations with deviated variables and to differential integral problems.

scholarly journals A PLANKTON ALLELOPATHIC MODEL DESCRIBED BY A DELAYED QUASILINEAR PARABOLIC SYSTEM

2012 ◽  
Vol 17 (4) ◽  
pp. 485-497 ◽  
Author(s):  
Canrong Tian ◽  
Peng Zhu
Keyword(s):  
Parabolic System ◽  
Upper And Lower Solutions ◽  
Asymptotically Stable ◽  
Stability Of Solutions ◽  
Quasilinear Parabolic System ◽  
Monotone Iterations ◽  
Engineering Problems ◽  
Existence And Stability ◽  
Uniform Equilibrium ◽  
Quasilinear Parabolic

The quasilinear parabolic system has been applied to a variety of physical and engineering problems. However, most works lack effective techniques to deal with the asymptotic stability. This paper is concerned with the existence and stability of solutions for a plankton allelopathic model described by a quasilinear parabolic system, in which the diffusions are density-dependent. By the coupled upper and lower solutions and its associated monotone iterations, it is shown that under some parameter conditions the positive uniform equilibrium is asymptotically stable. Some biological interpretations for our results are given.

scholarly journals Blow-Up and Global Existence for a Quasilinear Parabolic System

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Chunchen Wu
Keyword(s):  
Global Existence ◽  
Parabolic System ◽  
Blow Up ◽  
Quasilinear Parabolic System ◽  
Quasilinear Parabolic

The problem of solutions to a class of quasilinear coupling parabolic system was studied. By constructing weak upper-solutions and weak lower-solutions, we obtain the global existence and blow-up of solutions under appropriate conditions.

Well-posedness for coupled bulk-interface diffusion with mixed boundary conditions

Analysis ◽  
2015 ◽  
Vol 35 (4) ◽  
Author(s):  
Karoline Disser
Keyword(s):  
Boundary Conditions ◽  
Parabolic System ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Well Posedness ◽  
System Of Equations ◽  
Quasilinear Parabolic System ◽  
Interface Diffusion ◽  
Quasilinear Parabolic ◽  
Parabolic System Of Equations

AbstractIn this paper, we consider a quasilinear parabolic system of equations describing coupled bulk and interface diffusion, including mixed boundary conditions. The setting naturally includes non-smooth domains Ω. We show local well-posedness using maximal

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