Incompressible Laminar Flow Past a Transversely Vibrating Cylinder

1987 ◽  
Vol 109 (2) ◽  
pp. 166-171 ◽  
Author(s):  
R. Chilukuri
Keyword(s):  
Experimental Data ◽  
Laminar Flow ◽  
Finite Difference ◽  
Vortex Shedding ◽  
Lift Coefficient ◽  
Small Vibration ◽  
Flow Past ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Experimental Scatter

An implicit finite difference scheme in primitive variables is used for analysis of unsteady, laminar flow past transversely vibrating cylinders. Predictions of flow past an impulsively started cylinder and of vortex shedding from a stationary cylinder agree well with experimental data. Calculations of flow past a transversely vibrating cylinder were within the range of experimental scatter only for small vibration amplitudes. Several experimentally observed phenomena such as drag amplification and reduction in excitation lift coefficient at large vibration amplitudes were numerically predicted.

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.

scholarly journals Finite Difference Solution to a Nonlinear Time-Fractional Logistic Model

2021 ◽  
Vol 13 (2) ◽  
pp. 60
Author(s):  
Yuanyuan Yang ◽  
Gongsheng Li
Keyword(s):  
Finite Difference ◽  
Theoretical Analysis ◽  
Difference Scheme ◽  
Logistic Model ◽  
Stability And Convergence ◽  
Numerical Examples ◽  
Implicit Finite Difference Scheme ◽  
Finite Difference Solution ◽  
Implicit Finite Difference ◽  
Convergence Of The Scheme

We set forth a time-fractional logistic model and give an implicit finite difference scheme for solving of the model. The L^2 stability and convergence of the scheme are proved with the aids of discrete Gronwall inequality, and numerical examples are presented to support the theoretical analysis.

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