Journal ArticleDOI
Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
TLDR
These new formulas are suitable for the numerical integration of heat transfer problems after discretisation of these problems in the space variables, since stability considerations, occurring in such problems, would eliminate the benefits of high-orderRunge-Kutta formulas.Abstract:
Es werden neue, expliziteRunge-Kutta-Formeln vierter und niedrigerer Ordnung mitgeteilt. Diese Formeln enthalten eine Schrittweiten-Kontrolle, die auf einer vollstandigen Erfassung des ersten Gliedes des lokalen Abbruchfehlers basiert. Die Formeln haben wesentlich kleinere Abbruchfehler als entsprechende Formeln anderer Autoren. Diese neuen Formeln eignen sich zur numerischen Integration von in den Raumvariablen diskretisierten Warmeleitungsproblemen, da die bei solchen Problemen auftretenden Stabilitatsverhaltnisse die zulassige Schrittweite vonRunge-Kutta-Formeln hoherer Ordnung beeintrachtigen wurden. Die Formeln werden auf ein Beispiel fur ein Warmeleitungsproblem angewandt.read more
Citations
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Exploiting the sparsity in the solution of linear ordinary differential equations
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Mathematical modeling of nonlinear thermodynamics of nanoplates
TL;DR: In this article , the theory of nonlinear statics and dynamics of flexible plates, taking into account the modified couple stress theory and temperature field, is developed, and the convergence of the proposed algorithms is investigated depending on the number of finite elements and the time step.
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DissertationDOI
Using high-resolution modelling to improve the parameterisation of convection in a climate model
Journal ArticleDOI
Assessing the accuracy and efficiency of different order implicit and explicit integration schemes
Martí Lloret-Cabot,Daichao Sheng +1 more
TL;DR: In this article, a first order fully implicit integration scheme and four different order explicit substepping integration schemes with automatic error control are used to integrate the constitutive relations of a critical state model for saturated soils.
References
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Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Stepsize Control
TL;DR: Runge-Kutta formulas of high order with stepsize control through leading truncation error term through leading parallelogram error term.
Journal ArticleDOI
Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle
TL;DR: New explicit fifth- and seventh-orderRunge-Kutta formulas are derived that include a stepsize control procedure based on a complete coverage of the leading term of the local truncation error.