Journal ArticleDOI
Stability regions for one-step multiderivative methods in PECE mode with application to stiff systems
A.Q.M Khaliq,E.H. Twizell +1 more
TLDR
In this paper, a family of one-step multiderivative predictor-corrector methods were tested on a linear system where the matrix of coefficients has constant complex eigenvalues and on a stiff nonlinear system arising in reactor kinetics.Abstract:
Stability regions are plotted for certain members of a family of one-step multiderivative predictor-corrector methods developed by the authors in an earlier paper. The methods discussed are tested on a linear system where the matrix of coefficients has constant complex eigenvalues and on a stiff non-linear system arising in reactor kinetics.read more
Citations
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Journal ArticleDOI
Multiplicative Adams Bashforth---Moulton methods
Emine Misirli,Yusuf Gurefe +1 more
TL;DR: The multiplicative version of Adams Bashforth–Moulton algorithms for the numerical solution of multiplicative differential equations is proposed and truncation error estimation for these numerical algorithms is discussed.
Journal ArticleDOI
New efficient second derivative multistep methods for stiff systems
TL;DR: In this paper, a special class of second derivative multistep method (SDMM) is derived and the stability analysis of this class which is depending on free parameters is discussed.
Journal ArticleDOI
The Runge-Kutta method in geometric multiplicative calculus
Mustafa Riza,Hatice Aktöre +1 more
TL;DR: In this article, the derivation, applicability, and efficiency of the multiplicative Runge-Kutta method, derived in the framework of geometric multiplicative calculus, are discussed.
Journal ArticleDOI
New Solution Method for Electrical Systems Represented by Ordinary Differential Equation
TL;DR: This work is an application of bigeometric Runge–Kutta (BRK4) method aiming to solve differential equations with nonzero initial condition, and results confirm the application of BRK4 method in electrical circuit analysis.
Journal ArticleDOI
The Runge-Kutta Method in Geometric Multiplicative Calculus
Mustafa Riza,Hatice Aktöre +1 more
TL;DR: In this article, the authors present the derivation, applicability and efficiency of the Multiplicative Runge-Kutta Method, derived in the frame-work of geometric multiplicative calculus.
References
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Journal ArticleDOI
On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae
TL;DR: In this article, a class of extended backward differentiation formulae suitable for the approximate numerical integration of stiff systems of first order ordinary differential equations is derived and an algorithm is described whereby the required solution is predicted using a conventional backward differentiation scheme and then corrected using an extended backward differentiated scheme of higher order.
Journal ArticleDOI
On the solution ofy′=f(x,y) by a class of high accuracy difference formulae of low order
TL;DR: Differenzengleichungenk-ter Ordnung (k=1, 2, 3, 4), in diey and dessen Ableitungen bis zurl-ten ordnung(l=1.2, 2.3, 4) einbezogen sind, werden zur numerischen Integration der Differentialgleichungy′=f(x,y),y0=0 benutzt as discussed by the authors.
Journal ArticleDOI
One step multiderivative methods for first order ordinary differential equations
E. H. Twizell,A. Q. M. Khaliq +1 more
TL;DR: In this paper, a family of one-step multiderivative methods based on Pade approximants to the exponential function is developed for use in PECE mode and compared with well-known linear multi-step combinations and combinations using high accuracy Newton-Cotes quadrature formulas as correctors.
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