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Öğe A Fréchet derivative-based novel approach to option pricing models in illiquid markets(John Wiley and Sons Ltd, 2022) Gülen, Seda; Sarı, M.Nonlinear option pricing models have been increasingly concerning in financial industries since they build more accurate values by regarding more realistic assumptions such as transaction cost, market liquidity, or uncertain volatility. This study defines a nonclassical numerical method to effectively capture the behavior of the nonlinear option pricing model in illiquid markets where the implementation of a dynamic hedging strategy affects the price of the underlying asset. Unlike the conventional numerical approaches, this study describes a numerical scheme based on the Newton iteration technique and the Fréchet derivative for linearization of the model. The linearized time-dependent PDE is then discretized by a sixth-order finite difference scheme in space and a second-order trapezoidal rule in time. The computations revealed that the current approach appears to be somewhat more effective to some extent and at the same time economical for illustrative examples compared to the existing competitors. In addition, this method helps to prevent considering the convergence issues of the Newton approach applied to the nonlinear algebraic system. © 2021 John Wiley & Sons, Ltd.Öğe A new approach for the black-scholes model with linear and nonlinear volatilities(MDPI AG, 2019) Gülen, Seda; Popescu, C.; Sarı, M.Since financial engineering problems are of great importance in the academic community, effective methods are still needed to analyze these models. Therefore, this article focuses mainly on capturing the discrete behavior of linear and nonlinear Black-Scholes European option pricing models. To achieve this, this article presents a combined method; a sixth order finite difference (FD6) scheme in space and a third-order strong stability preserving Runge-Kutta (SSPRK3) over time. The computed results are compared with available literature and the exact solution. The computed results revealed that the current method seems to be quite strong both quantitatively and qualitatively with minimal computational effort. Therefore, this method appears to be a very reliable alternative and flexible to implement in solving the problem while preserving the physical properties of such realistic processes. © 2019 by the authors.Öğe A novel hybrid method based cubic B-spline for one-dimensional Stefan problem with moving PCM, size-dependent thermal conductivity and periodic boundary condition(Springer Heidelberg, 2022) Gülen, SedaPhase change materials (PCM) are substances that release and absorb sufficient energy at phase transition to provide useful heat or cooling. Stefan problems including PCM have many applications in science and engineering. Since an exact solution for this type of Stefan problem does not exist, tracking the moving boundary and obtaining accurate temperature distribution are still challenging issues in mathematical aspects. Therefore, in this paper, a new approach based on combining the cubic B-spline and a fourth-order compact finite difference scheme is developed to capture the behavior of the one-dimensional Stefan problem including moving PCM, variable thermal conductivity and periodic boundary condition. The proposed combined method in space and the Crank-Nicolson method in time are applied to the model after the moving domain is transformed into the fixed domain by the boundary immobilization method. The comparative results have seen a good agreement for a particular case. Besides, the stability of the scheme and the effect of the model parameters on the numerical solution are analyzed. The computations reveal that the new combined method is seen to pull up the accuracy of the model solutions and presents an efficient alternative solution to the model.Öğe An efficient hybrid method based on cubic B-spline and fourth-order compact finite difference for solving nonlinear advection-diffusion-reaction equations(Springer, 2023) Gülen, SedaThis paper proposes an efficient hybrid numerical method to obtain approximate solutions of nonlinear advection-diffusion-reaction (ADR) equations arising in real-world phenomena. The proposed method is based on finite differences for the approximation of time derivatives while a combination of cubic B-splines and a fourth-order compact finite difference scheme is used for spatial discretization with the help of the Crank-Nicolson method. Since desired accuracy and order of convergence cannot be reached using the traditional cubic B-spline method, to overcome this, the second-order derivatives are approximated using the unknowns and their first derivative approximations with the compact support. Thus, instead of expressing the second-order derivative in second-order accuracy, it is represented by the convergence of order four in the present method. The computed results revealed that this combined approach improves the accuracy of solutions of nonlinear ADR equations in comparison to up-to-date literature even using relatively larger step sizes. Besides, this method is seen to be capable of capturing the behavior of the models with very small viscosity values. The stability of the proposed method has been discussed by considering the matrix stability approach and it has been shown that the method is stable. In addition to the fact that the proposed method obtains sufficiently accurate solutions, another main superiority is its simplicity and applicability, which requires minimum computational effort.Öğe Analysing of Tuberculosis in Turkey through SIR, SEIR and BSEIR Mathematical Models(Taylor and Francis Ltd., 2021) Uçakan, Yasin; Gülen, Seda; Köklü, KevserSince mathematical models play a key role in investigating the dynamics of infectious diseases, many mathematical models for these diseases are developed. In this paper, it is aimed to determine the dynamics of Tuberculosis (TB) in Turkey, how much it will affect the future and the impact of vaccine therapy on the disease. For this purpose, three mathematical models (SIR, SEIR and BSEIR) in the literature are considered for the case of Turkey. The model parameters are obtained with TB reported data from 2005 to 2015 by using the least square method. The obtained results revealed that the basic reproduction ratio for all three models is less than 1. Moreover, the stability analysis of the models and sensitivity analysis of the model parameters are presented and discussed. Finally, the accuracy of results for all three models is compared and the effect of the vaccination rate is discussed. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.Öğe INVESTIGATION OF BOTANICAL COMPOSITION, FEED VALUE, ORGANIC MATTER DIGESTIBILITY AND NET ENERGY LACTATION OF GRASS SILAGE AT EARLY MATURITY STAGE BY IN VIVO AND IN VITRO METHODS(Corvinus Univ Budapest, 2022) Gülen, SedaThis study was carried out to determine botanical composition, nutritive value, organic matter digestibility (OMD) and net energy lactation (NEL) of grass ensiled at early (early maturity, first cut) stage of maturity. In vivo and in vitro (gas test) methods were both used. The feed material of the study was taken from the producers in three different regions of (Arisu, Edremit, Kurubas) Van province at the first cutting period (1 June). Approximately 1000 kg of grass was cut from each pasture with a mower. It was kept in plastic bins, closed tightly and turned upside down until the day the silos were opened. In addition, 0.25m2 areas were cut, divided into species when wet, and the rate of participation of species in yield was calculated. Chemical analyses and in vivo and in vitro (gas test) experiments were conducted on the silage which was opended on the 60th day after it had been ensiled. According to the analysis; silages obtained from Edremit, Kurubas and Arisu pastures contained 27.38%, 22.30%, 24.78%, of dry matter 9.51%, 14.76%, 14.27% of crude protein, respectively; in vivo OMD was found 70.70%, 79,17%, 55.85%, and in vitro OMD48 h was found 66.79%, 61.65%, 61.15%, respectively. At the same time, the correlation between in vivo OMD and in vitro OMD48 hour was found R2 0.99. It has been determined that Gramineae family is the dominant plant population in the pastures of Van province. In conclusion, it has been evaluated that grass ensiled at early maturity (first cut) stage increased organic matter digestibility of silages.Öğe The impact of wheat bran and molasses addition to caramba mix silage on feed value and in vitro organic matter digestibility(Elsevier B.V., 2023) Gülen, SedaBackground: The fermentation process in silage is an inherently uncontrolled process that results in significant nutritional losses. Supplementing silage with different additives may boost nutrient and energy recovery during fermentation, which in turn can boost animal productivity. However, the impact of wheat bran and molasses addition on feed value of caramba mix silage is unknown. Methods: This study determined the impact of molasses and wheat straw addition on fermentation and in vitro organic matter digestibility of caramba mix silage. Caramba was cut at harvest maturity and subjected to five different treatments, i.e., control, addition of 5% and 10% molasses, and addition of 5% and 10% wheat bran. Caramba mix and additives were mixed and ensiled into laboratory type 1 L glass containers. Silage fermentation, chemical and microbiological composition, and in vitro metabolic energy content in silages were determined 60 days after the initiation of treatments. Results: Different chemical and microbial properties of silage were significantly altered by the addition of molasses and wheat bran. The addition of 10% molasses resulted in the highest values of all measured traits of Caramba mix silage. The dry matter was 27.00%, 28.44%, 33.93%, 32.67%, and 30.61% in control, 5% molasses, 10% molasses, 5% wheat bran and 10% wheat bran, respectively. Similarly, pH was 5.32, 4.89, 4.56, 4.62, and 4.39 in control, 5% molasses, 10% molasses, 5% wheat bran and 10% wheat bran, respectively. Likewise, crude protein was 14.58%, 13.03%, 16.23%, 14.75%, and 16.42% in control, 5% molasses, 10% molasses, 5% wheat bran and 10% wheat bran, respectively. Conclusion: It is concluded that addition of molasses and wheat bran to the caramba mix silage increased the chemical, and microbiological qualities. Particularly molasses improved the digestibility of silage. Therefore, it is recommended that 10% molasses should be added during the fermentation of the silage to improve chemical, and microbiological properties of Caramba mix silage. © 2022 The Author(s)Öğe Valuation of the American put option as a free boundary problem through a high-order difference scheme(De Gruyter Open Ltd, 2021) Sarı, Murat; Gülen, SedaValuation of the American options encountered commonly in finance is quite difficult due to the possibility of early exercise alternatives. Since an exact solution for the American options does not exist, effective numerical methods are needed to understand the behavior of option pricing models. Therefore, in this paper, a new approach based on a high-order difference scheme is proposed to discuss the valuation of an American put option as a free boundary problem. Using a front-fixing approach that transforms the unknown free boundary (optimal stopping) into a fixed one, a sixth-order finite difference scheme (FD6) in space and a third-order strong-stability preserving Runge-Kutta (SSPRK3) in time are applied to the model converted to a nonlinear partial differential equation. The computed results revealed that the combined method is seen to attempt to pull up the capacity of the algorithm to achieve higher accuracy. It is seen that the quantitative and qualitative results produced by the method proposed with minimal computational effort are sufficiently accurate and meaningful. Therefore, this article provides some new insights about the physical characteristics of financial problems and such realistic phenomena. © 2021 Walter de Gruyter GmbH, Berlin/Boston.
