Fractional Crank-Nicolson finite difference method for benign brain tumor detection and segmentation

2020 ◽  
Vol 60 ◽  
pp. 102002
Author(s):  
Saroj Kumar Chandra ◽  
Manish Kumar Bajpai
Keyword(s):  
Brain Tumor ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Tumor Detection ◽  
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

scholarly journals A Newton Linearized Crank-Nicolson Method for the Nonlinear Space Fractional Sobolev Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yifan Qin ◽  
Xiaocheng Yang ◽  
Yunzhu Ren ◽  
Yinghong Xu ◽  
Wahidullah Niazi
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Scheme ◽  
Difference Method ◽  
Stability And Convergence ◽  
Sobolev Equation ◽  
Numerical Examples ◽  
Convergence Orders ◽  
Theoretical Results ◽  
Crank Nicolson

In this paper, one class of finite difference scheme is proposed to solve nonlinear space fractional Sobolev equation based on the Crank-Nicolson (CN) method. Firstly, a fractional centered finite difference method in space and the CN method in time are utilized to discretize the original equation. Next, the existence, uniqueness, stability, and convergence of the numerical method are analyzed at length, and the convergence orders are proved to be O τ 2 + h 2 in the sense of l 2 -norm, H α / 2 -norm, and l ∞ -norm. Finally, the extensive numerical examples are carried out to verify our theoretical results and show the effectiveness of our algorithm in simulating spatial fractional Sobolev equation.

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