Crank–Nicolson finite difference method for two-dimensional diffusion with an integral condition

2001 ◽  
Vol 124 (1) ◽  
pp. 17-27 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Integral Condition ◽  
Two Dimensional ◽  
Dimensional Diffusion ◽  
Crank Nicolson

scholarly journals A Comparative Study between Implicit and Crank-Nicolson Finite Difference Method for Option Pricing

2020 ◽  
Vol 40 (1) ◽  
pp. 13-27
Author(s):  
Tanmoy Kumar Debnath ◽  
ABM Shahadat Hossain
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Option Pricing ◽  
Difference Method ◽  
Finite Difference Methods ◽  
Put Option ◽  
Black Scholes ◽  
Implicit Finite Difference ◽  
Difference Methods ◽  
Crank Nicolson

In this paper, we have applied the finite difference methods (FDMs) for the valuation of European put option (EPO). We have mainly focused the application of Implicit finite difference method (IFDM) and Crank-Nicolson finite difference method (CNFDM) for option pricing. Both these techniques are used to discretized Black-Scholes (BS) partial differential equation (PDE). We have also compared the convergence of the IFDM and CNFDM to the analytic BS price of the option. This turns out a conclusion that both these techniques are fairly fruitful and excellent for option pricing. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 13-27

The Simplified Method to Calculate Two-Dimensional Heat Conduction Equations of Heating Slab

2011 ◽  
Vol 79 ◽  
pp. 105-110
Author(s):  
Guo Jun Li ◽  
Xiao Ting Li ◽  
Hai Geng Chen
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Thermal Flux ◽  
Computational Time ◽  
Fourth Power ◽  
Heating Process ◽  
Two Dimensional ◽  
Simplified Method

The most effective way of determining the whole billet temperature field is to use a simulation model. Large amount of calculation as well as computational time is consumed to employ two-dimensional finite difference method since the heating process is extremely complex, then it’s necessary to simplify the calculation process. In this paper, a simplified method in one-dimension format was presented to calculate two-dimensional heat conduction equations of heating slab. The billet simulated was placed in a changeable thermal flux boundary environment, in which the thermal flux was proportional to fourth power of temperature. During the heating process, the changeable parameters were taken into account: i. e different billet dimensions, different billet thermal conduction, different specific heat, etc. The comparision between results of two-dimensional finite difference method and the simplified method verified that the simplified method can satisfy accuracy requirement as well as calculation time saving, which enable the simplified method online using.

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