Year 2014,
Volume: 63 Issue: 1, 55 - 71, 01.02.2014
Abstract
In this paper, the method of the quasilinearization technique in
causal
differential equations is applied to obtain upper and lower sequences with
initial time difference in terms of the solutions of the linear causal differential
equations that start at different initial times. It is also shown that these
sequences converge to the unique solution of the nonlinear equation in causal
differential equations uniformly and superlinearly.
References
- Jankowski, T.: Quadratic Convergence of monotone iterations for diğerential equations with initial time diğerence. Dynamic Systems and Applications 14, 245-252 (2005).
- Köksal, S. and Yakar, C.: Generalized Quasilinearization Method with Initial Time Dif- ference, Simulation, an International Journal of Electrical, Electronic and other Physical Systems, 24 (5), (2002).
- Ladde, G.S, Lakshmikantham, V. and Vatsala, A.S.: Monotone Iterative Technique for Non- linear Diğerential Equations, Boston. Pitman Publishing Inc. 1985.
- Lakshmikantham, V. and Leela, S.: Nonlinear Diğerential Equations in Abstract Spaces, New York. Pergamon Press 1981.
- Lakshmikantham, V., Leela, S. Drici Z. and McRae F.A. : Theory of Causal Diğerential Equations, Amsterdam,World Scienti…c 2009.
- Lakshmikantham, V., Leela, S. and Vasundhara Devi, J.: Another Approach to the Theory of Diğerential Inequalities Relative to Changes in the Initial Times. Journal of Inequalities and Applications. 4, 163-174 (1999).
- Lakshmikantham, V. and Vatsala, A.S.: Diğerential Inequalities with Initial Time Diğerence and Applications. Journal of Inequalities and Applications. 3, 233-244 (1999).
- Lakshmikantham, V. and Vatsala, A.S.: Generalized Quasilinearization for Nonlinear Prob- lems, The Netherlands. Kluwer Academic Publisher 1998.
- Lakshmikantham, V. and Vatsala, A.S.: Theory of Diğerential and Integral Inequalities with Initial Time Diğerence and Applications. Analytic and Geometric Inequalities and Applica- tions Kluwer Academic Publishers, , 191-203 (1999).
- Yakar, C. and S.G., Deo.: Variation of Parameters Formulae with Initial Time Diğerence for Linear Integrodiğerential Equations. Journal of Applicable Analysis. Taylor & Francis.85, 333-343 (2006)
- Yakar, C. and Yakar, A.: An Extension of the Quasilinearization Method with Initial Time Diğerence. Dynamics of Continuous, Discrete and Impulsive Systems. Series A: Mathematical Analysis. Waterloo, Watam Press.14 (S2) 275-279 (2007).
- Yakar, C. and Yakar, A: Further Generalization of Quasilinearization Method with Initial Time Diğerence. Journal of Applied Functional Analysis. Eudoxus Press 4, 714-727. (2009). [13] Yakar, C. Initial Time Diğerence Quasilinearization Method in Banach Space. Journal of Communications in Mathematics and Applications. Volume 2 (2011) Number2-3, pp.77-85. Current address : Gebze Institute of Technology Faculty of Sciences, Department of Mathe- matics Applied Mathematics, Gebze-Kocaeli 141-41400, TURKEY
- E-mail address : cyakar@gyte.edu.tr
- URL: http://communications.science.ankara.edu.tr/index.php?series=A1
Year 2014,
Volume: 63 Issue: 1, 55 - 71, 01.02.2014
Abstract
References
- Jankowski, T.: Quadratic Convergence of monotone iterations for diğerential equations with initial time diğerence. Dynamic Systems and Applications 14, 245-252 (2005).
- Köksal, S. and Yakar, C.: Generalized Quasilinearization Method with Initial Time Dif- ference, Simulation, an International Journal of Electrical, Electronic and other Physical Systems, 24 (5), (2002).
- Ladde, G.S, Lakshmikantham, V. and Vatsala, A.S.: Monotone Iterative Technique for Non- linear Diğerential Equations, Boston. Pitman Publishing Inc. 1985.
- Lakshmikantham, V. and Leela, S.: Nonlinear Diğerential Equations in Abstract Spaces, New York. Pergamon Press 1981.
- Lakshmikantham, V., Leela, S. Drici Z. and McRae F.A. : Theory of Causal Diğerential Equations, Amsterdam,World Scienti…c 2009.
- Lakshmikantham, V., Leela, S. and Vasundhara Devi, J.: Another Approach to the Theory of Diğerential Inequalities Relative to Changes in the Initial Times. Journal of Inequalities and Applications. 4, 163-174 (1999).
- Lakshmikantham, V. and Vatsala, A.S.: Diğerential Inequalities with Initial Time Diğerence and Applications. Journal of Inequalities and Applications. 3, 233-244 (1999).
- Lakshmikantham, V. and Vatsala, A.S.: Generalized Quasilinearization for Nonlinear Prob- lems, The Netherlands. Kluwer Academic Publisher 1998.
- Lakshmikantham, V. and Vatsala, A.S.: Theory of Diğerential and Integral Inequalities with Initial Time Diğerence and Applications. Analytic and Geometric Inequalities and Applica- tions Kluwer Academic Publishers, , 191-203 (1999).
- Yakar, C. and S.G., Deo.: Variation of Parameters Formulae with Initial Time Diğerence for Linear Integrodiğerential Equations. Journal of Applicable Analysis. Taylor & Francis.85, 333-343 (2006)
- Yakar, C. and Yakar, A.: An Extension of the Quasilinearization Method with Initial Time Diğerence. Dynamics of Continuous, Discrete and Impulsive Systems. Series A: Mathematical Analysis. Waterloo, Watam Press.14 (S2) 275-279 (2007).
- Yakar, C. and Yakar, A: Further Generalization of Quasilinearization Method with Initial Time Diğerence. Journal of Applied Functional Analysis. Eudoxus Press 4, 714-727. (2009). [13] Yakar, C. Initial Time Diğerence Quasilinearization Method in Banach Space. Journal of Communications in Mathematics and Applications. Volume 2 (2011) Number2-3, pp.77-85. Current address : Gebze Institute of Technology Faculty of Sciences, Department of Mathe- matics Applied Mathematics, Gebze-Kocaeli 141-41400, TURKEY
- E-mail address : cyakar@gyte.edu.tr
- URL: http://communications.science.ankara.edu.tr/index.php?series=A1
There are 14 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | February 1, 2014 |
| Published in Issue | Year 2014 Volume: 63 Issue: 1 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
