A New Implicit Finite Difference Algorithm of Thermal Melt Flow in Filling Process Based on Projection Method

2012 ◽  
Vol 9 (9) ◽  
pp. 1374-1378 ◽  
Author(s):  
Xiaofeng Niu ◽  
Wei Liang ◽  
Yuhong Zhao ◽  
Hua Hou ◽  
Yanqing Mu ◽  
...  
Keyword(s):  
Finite Difference ◽  
Projection Method ◽  
Melt Flow ◽  
Filling Process ◽  
Implicit Finite Difference

scholarly journals A robust numerical solution to a time-fractional Black–Scholes equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. M. Nuugulu ◽  
F. Gideon ◽  
K. C. Patidar
Keyword(s):  
Finite Difference ◽  
Stock Options ◽  
Stochastic Dynamics ◽  
European Options ◽  
Numerical Convergence ◽  
Put Option ◽  
Implicit Finite Difference Scheme ◽  
Black Scholes ◽  
Implicit Finite Difference ◽  
Rigorous Mathematical Analysis

AbstractDividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work are appropriate for capturing market fluctuations in which random fractional white noise has the potential to accurately estimate European put option premiums while providing a good numerical convergence. The aim of this paper is two fold: firstly, to construct a time-fractional (tfBS) PDE for pricing European options on continuous dividend paying stocks, and, secondly, to propose an implicit finite difference method for solving the constructed tfBS PDE. Through rigorous mathematical analysis it is established that the implicit finite difference scheme is unconditionally stable. To support these theoretical observations, two numerical examples are presented under the proposed fractional framework. Results indicate that the tfBS and its proposed numerical method are very effective mathematical tools for pricing European options.

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