جستجوی مقالات مرتبط با کلیدواژه « numerical solutions » در نشریات گروه « ریاضی »
تکرار جستجوی کلیدواژه «numerical solutions» در نشریات گروه «علوم پایه»-
Journal of Mathematical Analysis and its Contemporary Applications, Volume:3 Issue: 4, Autumn 2021, PP 25 -40In this paper, an efficient numerical method based on operational matrices of the second kind Chebyshev polynomials is used for the solution of a coupled system of fractional-order integrodifferential equations that the fractional derivative is given in Caputo's sense. The operational matrices of the second kind Chebyshev polynomials reduce the given equations to a system of linear algebraic equations. An approximate solution is calculated by extending the functions in terms of the second kind Chebyshev polynomials and applying operational matrices. Unknown coefficients are obtained by solving the final system of linear equations. Also, convergence analysis and error bound of the solution are studied in this paper. Moreover, to check the reliability and accuracy of the given method. The numerical examples have been shown and the results of the described method are compared with the Haar wavelet method. The obtained results authenticate that the displayed method is effortless to analyze and perform such types of problems. All methods for the proposed method are applied in MATLAB (R2020b) software.Keywords: Integro differential equations, Operational matrix, Second kind Chebyshev polynomials, Numerical solutions}
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In this paper, the polynomial differential quadrature method (PDQM) is implemented to find the numerical solution of the generalized Black-Scholes partial differential equation. The PDQM reduces the problem into a system of first order non-linear differential equations and then, the obtained system is solved by optimal four-stage, order three strong stability-preserving time-stepping Runge-Kutta (SSP-RK43) scheme. Numerical examples are given to illustrate the efficiency of the proposed method.
Keywords: Option pricing, Generalized Black-Scholes equation, Numerical solutions, Polynomial differential quadrature method (PDQM), Runge-Kutta method} -
In this paper, we consider two dimensional nonlinear elliptic equations of the form −div(a(u,∇u))=f . Then, in order to solve these equations on rectangular domains, we propose a numerical method based on Sinc-Galerkin method. Finally, the presented method is tested on some examples. Numerical results show the accuracy and reliability of the proposed method.Keywords: Sinc-Galerkin method, elliptic partial differential equations, nonlinear problems, numerical solutions}
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In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.Keywords: Fractional Black-Schole, Numerical solutions, Finite di erence}
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