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Multiplicative finite difference methods
Author(s):
Mustafa
Riza;
Ali
Özyapici;
Emine
Misirli
Journal:
Quart. Appl. Math.
67
(2009),
745-754.
MSC (2000):
Primary 65L12;
Secondary 65N06
Posted:
May 14, 2009
MathSciNet review:
2588234
Retrieve article in:
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Abstract |
References |
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Additional information
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.
References:
-
- 1.
- M. Grossmann, R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts, 1972. MR 0430173 (55:3180)
- 2.
- V. Volterra, B. Hostinsky, Operations Infinitesimales Lineares, Gauthier-Villars, Paris, 1938.
- 3.
- M. Grossmann, Bigeometric Calculus, A System with a Scale-free Derivative, Archimedes Foundation, Rockport, 1983. MR 695495 (84h:26003)
- 4.
- 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)
- 5.
- 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
- 6.
- D. Aniszewska, Multiplicative Runge-Kutta methods, Nonlinear Dynamics 50 (1-2) (2007) 265-272.
- 7.
- 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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