157 research outputs found
Stability concepts and their applications
The stability is one of the most basic requirement for the numerical model, which is mostly elaborated for the linear problems. In this paper we analyze the stability notions for the nonlinear problems. We show that, in case of consistency, both the N-stability and K-stability notions guarantee the convergence. Moreover, by using the N-stability we prove the convergence of the centralized Crank-Nicolson-method for the periodic initial-value transport equation. The K-stability is applied for the investigation of the forward Euler method and the θ-method for the Cauchy problem with Lipschitzian right side. © 2014 Elsevier Ltd. All rights reserved
Linear multistep methods with repeated global Richardson
In this work, we further investigate the application of the well-known
Richardson extrapolation (RE) technique to accelerate the convergence of
sequences resulting from linear multistep methods (LMMs) for numerically
solving initial-value problems of systems of ordinary differential equations.
By extending the ideas of our previous paper, we now utilize some advanced
versions of RE in the form of repeated RE (RRE). Assume that the underlying LMM
-- the base method -- has order and RE is applied times. Then we prove
that the accelerated sequence has convergence order . The version we
present here is global RE (GRE, also known as passive RE), since the terms of
the linear combinations are calculated independently. Thus, the resulting
higher-order LMM-RGRE methods can be implemented in a parallel fashion and
existing LMM codes can directly be used without any modification. We also
investigate how the linear stability properties of the base method (e.g. -
or -stability) are preserved by the LMM-RGRE methods
Ă–njavĂtĂł házi feladatlapokban rejlĹ‘ lehetĹ‘sĂ©gek az angol nyelvĂłrán: Esettanulmány a magyar felsĹ‘oktatási kontextusban
One of the most prominent questions in education after the school closures during the Covid-19 pandemic is how to incorporate and ensure the presence of digital technologies in face-to-face education. There seems to be an agreement between scholars that learners are excellent users of technological tools regarding their entertainment potential, but they need instruction on how to use tools as autonomous learning aids. This case study aimed to explore how a set of digital, self-correcting homework tasks (N = 10) could aid learners in their studies as part of a first-year applied English grammar course at an English Studies programme of a Hungarian university. Another aim was to find out what potentials lie for the instructor in monitoring the effort students put into their out-of-class learning. The study used two data collecting tools, an end-of-course questionnaire with learners (N = 52) and the metadata of the ten digital task sheets downloaded from Google Forms. The results prove that learners mostly welcomed the immediate feedback and the straightforward nature of homework qualities of the tasks, but the results also show that first-year university groups can be quite heterogeneous as far as learners’ proficiency is concerned. Analysis of the metadata shows that the digital tasks engaged learners for approx. 50 minutes every week, which means that the difficulty of the tasks was balanced. Implications of this study might inspire instructors to try out such digital self-correcting tasks as part of their courses, which could also contribute to developing and updating the tasks over the course of time based on meta-analysis.A Covid–19 világjárvány iskolabezárásokkal járĂł hullámai után az oktatás egyik aktuális kĂ©rdĂ©se, hogy a digitális munkarendű oktatás során kiprĂłbált technolĂłgiák hogyan Ă©pĂthetĹ‘k be a jelenlĂ©ti oktatásba. A szakirodalom egyetĂ©rt abban, hogy a hallgatĂłk Ă©letkoruknál fogva többnyire kiválĂł ismeretekkel rendelkeznek a szĂłrakoztatĂł elektronika terĂĽletĂ©n, ám tudatosan, saját ismereteik fejlesztĂ©sĂ©re fĹ‘leg akkor tudják jĂłl használni eszközeiket, ha erre az oktatásuk során megtanĂtják Ĺ‘ket. Erre jĂł mĂłdszer lehet a digitális lehetĹ‘sĂ©gek integrálása a kurzusaikba. Jelen esettanulmány azt vizsgálta, mennyiben segĂti a hallgatĂłkat Ă©s milyen mĂ©lysĂ©gű bepillantást tesz lehetĹ‘vĂ© az oktatĂł számára a hallgatĂłi otthoni munkába a Google Ĺ°rlapok felĂĽletĂ©n lĂ©trehozott tĂz darab önjavĂtĂł házi feladatlap, amely egy elsĹ‘Ă©ves angol szakos alkalmazott nyelvtan kurzushoz kapcsolĂłdott. A kutatás kĂ©t adatgyűjtĹ‘ eszközre, egy kurzusvĂ©gi hallgatĂłi kĂ©rdĹ‘Ăvre (N = 52) Ă©s a házi feladatlapok metaadataira (N = 10) támaszkodott. Az eredmĂ©nyek arrĂłl árulkodnak, hogy a hallgatĂłk az azonnali visszajelzĂ©st Ă©s az egyĂ©rtelműsĂ©get kedveltĂ©k a legjobban az önjavĂtĂł online házi feladatlapokban, ugyanakkor az elsĹ‘s egyetemi kurzusok heterogenitására utal, hogy nem minden hallgatĂł számára igĂ©nyelt azonos befektetĂ©st azok megoldása. A metaadatok elemzĂ©se azt mutatta, hogy a feladatlapok nagyjábĂłl megfelelĹ‘ nehĂ©zsĂ©gűnek bizonyultak, Ă©s kitöltĂ©sĂĽk átlagosan kb. 50 percet vett igĂ©nybe hetente. Az esettanulmány tapasztalatai más oktatĂłk számára is inspiráciĂłt jelenthetnek kurzusaik kiegĂ©szĂtĂ©sĂ©re hasonlĂł feladatlapokkal, valamint hozzájárulhatnak a házi feladatlapok folyamatos továbbfejlesztĂ©sĂ©hez, miközben összetett bepillantást nyĂşjtanak az otthoni munkavĂ©gzĂ©sbe
Dupla kompozitok gyártása, valamint mikroszerkezeti és mechanikai tulajdonságai
CikkĂĽnkben olyan fĂ©mmátrixĂş kompozitokkal foglalkozunk, amelyek kĂ©t kĂĽlönbözĹ‘ kompozit (egy kompozit huzal Ă©s egy szintaktikus fĂ©mhab) egyesĂtĂ©sĂ©vel jönnek lĂ©tre. Mivel a huzal már önmagában is kompozit, a kompozit tömbökre dupla kompozitokkĂ©nt hivatkozunk. Munkánk során sikeresen állĂtottunk elĹ‘ dupla kompozitokat gáznyomásos infiltrálással. Az előállĂtott dupla kompozitokat mikroszerkezeti Ă©s mechanikai vizsgálatoknak vetettĂĽk alá. A mikroszerkezeti vizsgálataink során elsĹ‘sorban az infiltráciĂł szintjĂ©t, Ă©s a határrĂ©tegek minĹ‘sĂ©gĂ©t követtĂĽk nyomon. A kĂ©sz dupla kompozit alapanyagábĂłl kĂ©szĂtettĂĽnk referenciadarabokat is, amelyekhez viszonyĂtottuk a kĂĽlönbözĹ‘ erĹ‘sĂtĂ©si struktĂşrájĂş dupla kompozitok mechanikai vizsgálatainak eredmĂ©nyeit. Az eredmĂ©nyek azt mutatták, hogy bár abszolĂşt tekintetben a tömör referenciadarab mutatĂłi jobbak, tömegre fajlagosĂtva a dupla kompozitok eredmĂ©nyei bĂztatĂłak
Embedded error estimation and adaptive step-size control for optimal explicit strong stability preserving Runge--Kutta methods
We construct a family of embedded pairs for optimal strong stability
preserving explicit Runge-Kutta methods of order to be used
to obtain numerical solution of spatially discretized hyperbolic PDEs. In this
construction, the goals include non-defective methods, large region of absolute
stability, and optimal error measurement as defined in [5,19]. The new family
of embedded pairs offer the ability for strong stability preserving (SSP)
methods to adapt by varying the step-size based on the local error estimation
while maintaining their inherent nonlinear stability properties. Through
several numerical experiments, we assess the overall effectiveness in terms of
precision versus work while also taking into consideration accuracy and
stability.Comment: 22 pages, 49 figure
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