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pro vyhledávání: '"Izgin, Thomas"'
A Boot-Strapping Technique to Design Dense Output Formulae for Modified Patankar-Runge-Kutta Methods
Autor:
Izgin, Thomas
In this work modified Patankar-Runge-Kutta (MPRK) schemes up to order four are considered and equipped with a dense output formula of appropriate accuracy. Since these time integrators are conservative and positivity preserving for any time step size
Externí odkaz:
http://arxiv.org/abs/2406.16718
Autor:
Izgin, Thomas
The work deals with two major topics concerning the numerical analysis of Runge-Kutta-like (RK-like) methods, namely their stability and order of convergence. RK-like methods differ from additive RK methods in that their coefficients are allowed to d
Externí odkaz:
http://arxiv.org/abs/2402.13788
Autor:
Izgin, Thomas, Ranocha, Hendrik
Modified Patankar--Runge--Kutta (MPRK) methods are linearly implicit time integration schemes developed to preserve positivity and a linear invariant such as the total mass in chemical reactions. MPRK methods are naturally equipped with embedded sche
Externí odkaz:
http://arxiv.org/abs/2312.01796
Recently, a stability theory has been developed to study the linear stability of modified Patankar--Runge--Kutta (MPRK) schemes. This stability theory provides sufficient conditions for a fixed point of an MPRK scheme to be stable as well as for the
Externí odkaz:
http://arxiv.org/abs/2309.01562
In recent years, many positivity-preserving schemes for initial value problems have been constructed by modifying a Runge--Kutta (RK) method by weighting the right-hand side of the system of differential equations with solution-dependent factors. The
Externí odkaz:
http://arxiv.org/abs/2305.14297
In this paper we investigate the stability properties of the so-called gBBKS and GeCo methods, which belong to the class of nonstandard schemes and preserve the positivity as well as all linear invariants of the underlying system of ordinary differen
Externí odkaz:
http://arxiv.org/abs/2301.10658
Modified Patankar (MP) schemes are conservative, linear implicit and unconditionally positivity preserving time-integration schemes constructed for production-destruction systems. For such schemes, a classical stability analysis does not yield any in
Externí odkaz:
http://arxiv.org/abs/2211.08905
Modified Patankar-Runge-Kutta (MPRK) methods preserve the positivity as well as conservativity of a production-destruction system (PDS) of ordinary differential equations for all time step sizes. As a result, higher order MPRK schemes do not belong t
Externí odkaz:
http://arxiv.org/abs/2210.11845
A study of the local dynamics of modified Patankar DeC and higher order modified Patankar RK methods
Autor:
Izgin, Thomas, Öffner, Philipp
Patankar schemes have attracted increasing interest in recent years because they preserve the positivity of the analytical solution of a production-destruction system (PDS) irrespective of the chosen time step size. Although they are now of great int
Externí odkaz:
http://arxiv.org/abs/2206.07371
In this paper, we perform stability analysis for a class of second and third order accurate strong-stability-preserving modified Patankar Runge-Kutta (SSPMPRK) schemes, which were introduced in [4,5] and can be used to solve convection equations with
Externí odkaz:
http://arxiv.org/abs/2205.01488