Yazar "Gulen, Seda" seçeneğine göre listele

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    A Numerical Discussion for the European Put Option Model
    (2021) Gulen, Seda
    The Black-Scholes equations have been increasingly popular over the last three decades since they provide more practical information for optional behaviours. Therefore, effective methods have been needed to analyse these models. This study will mainly focus on investigating the behaviour of the Black-Scholes equation for the European put option pricing model. To achieve this, numerical solutions of the Black-Scholes European option pricing model are produced by three combined methods. Spatial discretization of the Black-Scholes model is performed using a fourth-order finite difference (FD4) scheme that allows a highly accurate approximation of the solutions. For the time discretization, three numerical techniques are proposed: a strong-stability preserving Runge Kutta (SSPRK3), a fourth-order Runge Kutta (RK4) and a one-step method. The results produced by the combined methods have been compared with available literature and the exact solution. It has seen that the results with minimal computational effort are sufficiently accurate.
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    An investigation on the estimation of the impact factors of pandemic deaths with artificial neural network and multiple regression algorithms: Covid-19 case
    (Yildiz Technical Univ, 2024) Demir, Ibrahim; Sari, Murat; Gulen, Seda; Balacescu, Aniela
    This article aims to successfully estimate the number of deaths in a pandemic, with the appropriate implementation of two new modelling approaches, artificial neural network and multiple regression analysis. Then, these methods have been used comparatively to predict death cases for the future course of the COVID-19 outbreak. These approaches proposed for estimation appear to result in few errors and perform well in providing information on the course of deaths in the epidemic. The agreement between the predicted results by these methods, and the actual data proves the superiority of the proposed ones in forecasting accuracy in future cases. This is expected to provide significant benefits in increasing the effectiveness of health policies to be implemented within the scope of the measures to be taken for the future of this and similar epidemics. As this investigation reveals that the current modelling methods have undeniable advantages in predicting epidemic trends, using our models is believed to provide an accurate estimate of death rates and guide policymakers in formulating research, health, socio-economic and fiscal policies. All these findings can be widely regarded as significant milestones and essential guides for researchers examining potential future epidemic tendencies. In addition, although this epidemic is quite complex and varies from country-to-country and various factors, the proposed approaches offer a great opportunity to model the outbreak in other epidemics as well as in other countries.
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    Solution of a Moving Boundary Problem for Soybean Hydration by Numerical Approximation
    (De Gruyter, 2020) Gulen, Seda; Ozis, Turgut
    Mass or heat transfer may cause volume variation, and the food hydration model is one of them that undergoes hydration (or drying) conveying volume change. In this paper, the numerical approximate solution based on an integral method has been presented for soybean hydration model. Trace of the moving boundary and unknown moisture content at the center of the grain have been determined. The obtained results are well matched with numerical solutions in the literature. © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.
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    Various optimized artificial neural network simulations of advection-diffusion processes
    (Iop Publishing Ltd, 2024) Sari, Murat; Gulen, Seda; Celenk, Pelin
    The aim of this research is to describe an artificial neural network (ANN) based method to approximate the solutions of the natural advection-diffusion equations. Although the solutions of these equations can be obtained by various effective numerical methods, feed forward neural network (FFNN) techniques combined with different optimization techniques offer a more practicable and flexible alternative than the traditional approaches to solve those equations. However, the ability of FFNN techniques to solve partial differential equations is a questionable issue and has not yet been fully concluded in the existing literature. The reliability and accuracy of computational results can be advanced by the choice of optimization techniques. Therefore, this study aims to take an effective step towards presenting the ability to solve the advection-diffusion equations by leveraging the inherent benefits of ANN methods while avoiding some of the limitations of traditional approaches. In this technique, the solution process requires minimizing the error generated by using a differential equation whose solution is considered as a trial solution. More specifically, this study uses a FFNN and backpropagation technique, one of the variants of the ANN method, to minimize the error and the adjustment of parameters. In the solution process, the loss function (error) needs to be minimized; this is accomplished by fitting the trial function into the differential equation using appropriate optimization techniques and obtaining the network output. Therefore, in this study, the commonly used techniques in the literature, namely gradient descent (GD), particle swarm optimization (PSO) and artificial bee colony (ABC), are selected to compare the effectiveness of gradient and gradient-free optimization techniques in solving the advection-diffusion equation. The calculations with all three optimization techniques for linear and nonlinear advection-diffusion equations have been run several times to obtain the optimum accuracy of the results. The computed results are seen to be very promising and in good agreement with the effective numerical methods and the physics-informed neural network (PINN) method in the literature. It is also concluded that the PSO-based algorithm outperforms other methods in terms of accuracy.