Szemináriumok

On the zero-stability of multistep methods on smooth nonuniform grids

Időpont: 
2017. 10. 12. 10:15
Hely: 
H306
Előadó: 
Imre Fekete (Eötvös Loránd University & MTA-ELTE NUMNET)
A szeminárium részletei: 
Farkas Miklós Alkalmazott Analízis Szeminárium

In order to be convergent, linear multistep methods must be zero stable. While constant step size theory was established in the 1950’s, zero stability on nonuniform grids is less well understood. Here we investigate zero stability on compact intervals and smooth nonuniform grids. The grid points are constructed as the image of an equidistant grid under a smooth deformation map. We show that for all strongly stable linear multistep methods, there is an $N^*$ such that a condition of zero stability is always fulfilled for $N > N^*$ under a smoothness condition. Examples are given for Adams and BDF type methods.

An explicit analytic solution of a coupled first order partial and ordinary differential equation system for a discontinuous initial-boundary value problem

Időpont: 
2017. 10. 05. 10:15
Hely: 
H306
Előadó: 
Zachár András
A szeminárium részletei: 
Farkas Miklós Alkalmazott Analízis Szeminárium

Non-polynomial series solution of a coupled first order partial and ordinary differential equation (PDE-ODE) system for a discontinuous initial and boundary condition has been developed. Linear equation systems are constructed to calculate the constant coefficients of the series solution. Explicit expressions have been found to the solution of these linear equation systems. Different forms of the solution have been compared to the numerical solution of the PDE-ODE system and the rate of the convergence is also investigated. The studied first order PDE-ODE system describes an unsteady convection dominated heat transfer process induced by a buoyant plume entrainment.

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