Quarterly of Applied Mathematics Quarterly of Applied Mathematics
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Multiplicative finite difference methods

Author(s): Mustafa Riza; Ali Özyapici; Emine Misirli
Journal: Quart. Appl. Math.
MSC (2000): Primary 65L12; Secondary 65N06
Posted: May 14, 2009
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Abstract: Based on multiplicative calculus, the finite difference schemes for the numerical solution of multiplicative differential equations and Volterra differential equations are presented. Sample problems were solved using these new approaches.

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M. Grossmann, R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts, 1972. MR 0430173 (55:3180)

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V. Volterra, B. Hostinsky, Operations Infinitesimales Lineares, Gauthier-Villars, Paris, 1938.

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M. Grossmann, Bigeometric Calculus, A System with a Scale-free Derivative, Archimedes Foundation, Rockport, 1983. MR 695495 (84h:26003)

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A. Bashirov, E. Kurpınar, A. Özyapıcı, Multiplicative calculus and its applications, Journal of Mathematical Analysis and Applications 337 (1) (2008) 36-48. MR 2356052 (2008k:26001)

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M. Ryabczuk, A. Kedzia, W. Zielinski, The concept of physical and fractal dimension II. The differential calculus in dimensional spaces, Chaos Solitons Fractals 12 (2001) 2537-2552. MR 1851077

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D. Aniszewska, Multiplicative Runge-Kutta methods, Nonlinear Dynamics 50 (1-2) (2007) 265-272.

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W. Kasprzak, B. Lysik, M. Rybaczuk, Dimensions, invariants models and fractals, in: Ukranian Society on Fracture Mechanics SPOLOM, Wroclaw-Lviv, Poland, 2004.

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Additional Information:

Mustafa Riza
Affiliation: Department of Mathematics, Eastern Mediterranean University, Gazimagusa - North Cyprus, via Mersin 10, Turkey
Email: mustafa.riza@emu.edu.tr

Ali Özyapici
Affiliation: Department of Mathematics, Ege University, Bornova, Izmir, Turkey
Email: ali.ozyapici@emu.edu.tr

Emine Misirli
Affiliation: Department of Mathematics, Ege University, Bornova, Izmir, Turkey
Email: emine.kurpinar@ege.edu.tr

PII: S0033-569X-09-01158-2
Keywords: Finite difference method, multiplicative calculus, Volterra calculus, bigeometric calculus
Received by editor(s): August 24, 2008
Posted: May 14, 2009
Additional Notes: The first author was supported by the A-Type Research Grant of Eastern Mediterranean University
Copyright of article: Copyright 2009, Brown University
The copyright for this article reverts to public domain after 28 years from publication.


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