scholarly journals On numerical solution by method of V.K. Dzyadyk of Goursat problem with constant coefficients

2021 ◽  
pp. 109
Author(s):  
V.P. Burlachenko ◽  
Yu.I. Romanenko
Keyword(s):  
Numerical Solution ◽  
Goursat Problem ◽  
Approximative Method ◽  
Generalized Polynomial ◽  
Constant Coefficients ◽  
Efficient Estimate

By means of Fourier-Chebyshev operators we construct, by approximative method, the generalized polynomial that approximates the solution of Goursat problem with constant coefficients. We obtain the efficient estimate of this approximation.

scholarly journals Transforming Arithmetic Asian Option PDE to the Parabolic Equation with Constant Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Zieneb Ali Elshegmani ◽  
Rokiah Rozita Ahmad ◽  
Saiful Hafiza Jaaman ◽  
Roza Hazli Zakaria
Keyword(s):  
Parabolic Equation ◽  
Analytical Solution ◽  
Heat Equation ◽  
Numerical Solution ◽  
Closed Form ◽  
Asian Option ◽  
Asian Options ◽  
New Approach ◽  
Constant Coefficients ◽  
Closed Form Analytical Solution

Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low volatility level. In this paper, we analyze the value of the arithmetic Asian option with a new approach using means of partial differential equations (PDEs), and we transform the PDE to a parabolic equation with constant coefficients. It has been shown previously that the PDE of the arithmetic Asian option cannot be transformed to a heat equation with constant coefficients. We, however, approach the problem and obtain the analytical solution of the arithmetic Asian option PDE.

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