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pro vyhledávání: '"65L05"'
In this paper an asymptotic expansion of the global error on the stepsize for partitioned linear multistep methods is proved. This provides a tool to analyse the behaviour of these integrators with respect to error growth with time and conservation o
Externí odkaz:
http://arxiv.org/abs/2411.13487
Parallel-in-time (PinT) techniques have been proposed to solve systems of time-dependent differential equations by parallelizing the temporal domain. Among them, Parareal computes the solution sequentially using an inaccurate (fast) solver, and then
Externí odkaz:
http://arxiv.org/abs/2411.06225
Autor:
Hanke, Michael, März, Roswitha
In contrast to regular ordinary differential equations, the problem of accurately setting initial conditions just emerges in the context of differential-algebraic equations where the dynamic degree of freedom of the system is smaller than the absolut
Externí odkaz:
http://arxiv.org/abs/2410.19585
Autor:
Carrel, Benjamin
This paper introduces new dynamical low-rank (DLR) methods for solving large-scale matrix differential equations, motivated by algorithms from randomised numerical linear algebra. The new methods consist essentially of two steps: a range estimation s
Externí odkaz:
http://arxiv.org/abs/2410.17091
Autor:
Popov, I. S.
A numerical method ADER-DG with a local DG predictor for solving a DAE system has been developed, which was based on the formulation of ADER-DG methods using a local DG predictor for solving ODE and PDE systems. The basis functions were chosen in the
Externí odkaz:
http://arxiv.org/abs/2410.04018
In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the analytical
Externí odkaz:
http://arxiv.org/abs/2409.20369
Nordic skiing provides fascinating opportunities for mathematical modelling studies that exploit methods and insights from physics, applied mathematics, data analysis, scientific computing and sports science. A typical ski course winds over varied te
Externí odkaz:
http://arxiv.org/abs/2410.02767
Autor:
Popov, I. S.
Publikováno v:
J. Sci. Comput. 100, 22 (2024)
An adaptation of the arbitrary high order ADER-DG numerical method with local DG predictor for solving the IVP for a first-order non-linear ODE system is proposed. The proposed numerical method is a completely one-step ODE solver with uniform steps,
Externí odkaz:
http://arxiv.org/abs/2409.09933
Autor:
Deeb, Ahmad, Dutykh, Denys
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic one-step numeri
Externí odkaz:
http://arxiv.org/abs/2409.10548
Autor:
Nikolić, Vanja, Rauscher, Teresa
Ultrasound contrast imaging is a specialized imaging technique that applies microbubble contrast agents to traditional medical sonography, providing real-time visualization of blood flow and vessels. Gas-filled microbubbles are injected into the body
Externí odkaz:
http://arxiv.org/abs/2408.06108