Journal ArticleDOI
Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
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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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EMHD time-dependant tangent hyperbolic nanofluid flow by a convective heated Riga plate with chemical reaction:
A. Mahdy,G. A. Hoshoudy +1 more
TL;DR: In this article, the boundary layer electro-magnetohydrodynamic (EMHD) flow of time-dependant non-Newtonian tangent hyperbolic nanofluid that is electrically conducting past a Riga...
Journal ArticleDOI
An inexact Newton method for nonlinear two-point boundary-value problems
TL;DR: The method of quasilinearization for nonlinear two-point boundary-value problems is an application of Newton's method to a nonlinear differential operator equation as mentioned in this paper, and conditions on size of the relative residual of the linear differential equation can then be specified to guarantee rapid local convergence to the solution of the nonlinear continuous problem.
Journal ArticleDOI
Kinetic analysis of a general model of activation of aspartic proteinase zymogens.
Ramón Varón,Manuela García-Moreno,D. Valera-Ruipérez,Francisco Garcia-Molina,F. García-Cánovas,R.G. Ladrón-de Guevara,J. Masiá-Pérez,Bent H. Havsteen +7 more
TL;DR: An experimental design and kinetic data analysis is suggested to estimate the kinetic parameters involved in the reaction mechanism proposed and a way to predict the time course of the relative contribution as well as the effect of the initial zymogen and activating enzyme concentrations, on the relative weight is suggested.
Journal ArticleDOI
A Neural Network Technique for the Derivation of Runge–Kutta Pairs Adjusted for Scalar Autonomous Problems
Vladislav N. Kovalnogov,Ruslan V. Fedorov,Yuri A. Khakhalev,T. E. Simos,Charalampos Tsitouras +4 more
TL;DR: This work considers the scalar autonomous initial value problem as solved by an explicit Runge–Kutta pair of orders 6 and 5, and concludes with a method which outperforms other pairs of the same two orders in a variety of scalar autonomy problems.
Journal ArticleDOI
Comparative Study of Matlab ODE Solvers for the Korakianitis and Shi Model
TL;DR: This work evaluated the dependence of the computed result, accuracy of the method, computational cost and execution time of all the solvers, on relative tolerance and initial time steps of the Korakianitis and Shi heart valve model over a cardiac cycle.
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.