Journal of New Researches in Mathematics
,
Issue17,Year,
Spring
2019
در این مقاله، روشی عددی برای حل معادلات دیفرانسیل مرتبه پیشنهاد شده است. تاکنون روشهای زیادی برای حل معادلات دیفرانسیل فازی مرتبه اول، توسط محققین ارائه شده است. اما روشهای عددی کمتری نسبت به روشهای مرتبه اول، برای حل معادلات دیفرانسیل فازی مرتبه با More
در این مقاله، روشی عددی برای حل معادلات دیفرانسیل مرتبه پیشنهاد شده است. تاکنون روشهای زیادی برای حل معادلات دیفرانسیل فازی مرتبه اول، توسط محققین ارائه شده است. اما روشهای عددی کمتری نسبت به روشهای مرتبه اول، برای حل معادلات دیفرانسیل فازی مرتبه بالا پیشنهاد شده است. در این تحقیق، ابتداء معادله دیفرانسیل مرتبه n به دستگاهی از معادلات دیفرانسیل فازی مرتبه اول تبدیل میشود، سپس از روش آدامز- بشفورث برای حل این دستگاه معادلات استفاده میشود. نهایتاً با ارائه مثالهایی، دقت روش سنجیده میشود.
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Theory of Approximation and Applications
,
Issue1,Year,
Spring
2018
In recent years, Fuzzy differential equations are very useful indifferent sciences such as physics, chemistry, biology and economy. It should be noted, that if the equations that appear to be uncertain, then take help of fuzzy logic at these equations. Considering that More
In recent years, Fuzzy differential equations are very useful indifferent sciences such as physics, chemistry, biology and economy. It should be noted, that if the equations that appear to be uncertain, then take help of fuzzy logic at these equations. Considering that most of the time analytic solution of such equations and finding an exact solution has either high complexity or cannot be solved, we applied numerical methods for the solution. The topics of fuzzy differential equations have been rapidly growing in recent years. So far, many methods have been presented to solve the first-order differential equations. Not many studies have been conducted for numerical solution of high-order fuzzy differential equations. In this research, first, the equation by reducing time, we become the first-order equation. Then we have applied Adam-Moulton multi-step methods for the initial approximation of one order differential equations. Finally, we examine the accuracy of method by presenting examples.
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Theory of Approximation and Applications
,
Issue1,Year,
Spring
2021
In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equationsof the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and converta two-dimensional fuzzy Fredholm integral equation to system o More
In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equationsof the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and converta two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equationsof the second kind in crisp case. We can use Adomian decomposition method for nding the approximationsolution of the each equation, hence obtain an approximation for fuzzy solution of 2D-FFIE-2. We prove theconvergence of the method and nally apply the method to some examples
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Theory of Approximation and Applications
,
Issue1,Year,
Spring
2020
Fuzzy Volterra integral equations, especially the second kind is interested for researchers to be solved withnumerical methods since analytical methods are not applicable. Here a new study based on Fibonacci polynomialscollocation method in order to solve them is introd More
Fuzzy Volterra integral equations, especially the second kind is interested for researchers to be solved withnumerical methods since analytical methods are not applicable. Here a new study based on Fibonacci polynomialscollocation method in order to solve them is introduced. Some properties of these polynomials are consideredto implement a collocation method in order to approximate the solution of Fuzzy Volterra integral equations ofthe second kind. The existence and uniqueness of the solution also convergence and error analysis of proposedmethod are proved thoroughly. The results showed the calculations of the method are simple and low cost.
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Theory of Approximation and Applications
,
Issue1,Year,
Winter
2022
In this paper, we want to solve the Fredholm integral equations of the second type using thenumerical finite differences method. In this method, we use the forward, central and backwardoperator’s to solve integral equations, and finally we compare these methods wi More
In this paper, we want to solve the Fredholm integral equations of the second type using thenumerical finite differences method. In this method, we use the forward, central and backwardoperator’s to solve integral equations, and finally we compare these methods with the help of nu-merical examples.
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Advances in Mathematical Finance and Applications
,
Issue4,Year,
Summer
2022
The primary goal of option pricing theory is to calculate the probability that an option will be exercised at expiration and assign a dollar value to it. Options pricing theory also derives various risk factors or sensitivities based on those inputs, since market condit More
The primary goal of option pricing theory is to calculate the probability that an option will be exercised at expiration and assign a dollar value to it. Options pricing theory also derives various risk factors or sensitivities based on those inputs, since market conditions are constantly changing, these factors provide traders with a means of determining how sensitive a specific trade is to price fluctuations, volatility fluctuations, and the passage of time. In this study, we derive a new exact solution for pricing European options using Kurganov-Tadmor when the underlying process follows the constant elasticity of variance model. This method was successfully applied to nonlinear convection-diffusion equations by Kurganov and Tadmor. Also, we provide computational results showing the performance of the method for European option pricing problems. The results showed that the proposed method is convenient to calculate the option price for K=3,β=(-3)/4,and N=200.
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