scholarly journals An adaptive moving mesh method for a time-fractional Black–Scholes equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jian Huang ◽  
Zhongdi Cen ◽  
Jialiang Zhao
Keyword(s):  
Error Analysis ◽  
Numerical Method ◽  
A Priori ◽  
Moving Mesh ◽  
Moving Mesh Method ◽  
Monitor Function ◽  
Black Scholes ◽  
Domain Boundaries ◽  
Adaptive Moving Mesh Method ◽  
Numerical Difficulty

AbstractIn this paper we study the numerical method for a time-fractional Black–Scholes equation, which is used for option pricing. The solution of the fractional-order differential equation may be singular near certain domain boundaries, which leads to numerical difficulty. In order to capture the singular phenomena, a numerical method based on an adaptive moving mesh is developed. A finite difference method is used to discretize the time-fractional Black–Scholes equation and error analysis for the discretization scheme is derived. Then, an adaptive moving mesh based on an a priori error analysis is established by equidistributing monitor function. Numerical experiments support these theoretical results.

A Moving Mesh Method for Kinetic/Hydrodynamic Coupling

2012 ◽  
Vol 4 (06) ◽  
pp. 685-702 ◽  
Author(s):  
Zhicheng Hu ◽  
Heyu Wang
Keyword(s):  
Coupling Model ◽  
Two Dimensions ◽  
Smooth Transition ◽  
Moving Mesh ◽  
Moving Mesh Method ◽  
Rapid Variation ◽  
Mesh Motion ◽  
Monitor Function ◽  
Hydrodynamic Coupling ◽  
Mesh Method

AbstractThis paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions. With some criteria, the domain is dynamically decomposed into three parts: kinetic regions where fluids are far from equilibrium, hydrodynamic regions where fluids are near thermody-namical equilibrium and buffer regions which are used as a smooth transition. The Boltzmann-BGK equation is solved in kinetic regions, while Euler equations in hydrodynamic regions and both equations in buffer regions. By a well defined monitor function, our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions. In each moving mesh step, the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion. In such a framework, the evolution of the hybrid model and the moving mesh procedure can be implemented independently, therefore keep the advantages of both approaches. Numerical examples are presented to demonstrate the efficiency of the method.

scholarly journals An Adaptive Moving Mesh Method for Forced Curve Shortening Flow

2019 ◽  
Vol 41 (2) ◽  
pp. A1170-A1200 ◽  
Author(s):  
J. A. Mackenzie ◽  
M. Nolan ◽  
C. F. Rowlatt ◽  
R. H. Insall
Keyword(s):  
Moving Mesh ◽  
Moving Mesh Method ◽  
Curve Shortening Flow ◽  
Mesh Method ◽  
Adaptive Moving Mesh Method ◽  
Curve Shortening

An Adaptive Moving Mesh Method for Two-Dimensional Relativistic Hydrodynamics

2012 ◽  
Vol 11 (1) ◽  
pp. 114-146 ◽  
Author(s):  
Peng He ◽  
Huazhong Tang
Keyword(s):  
Iterative Procedure ◽  
Moving Mesh ◽  
Finite Volume Scheme ◽  
Relativistic Hydrodynamics ◽  
Two Dimensional ◽  
Moving Mesh Method ◽  
Governing Equations ◽  
Nonuniform Meshes ◽  
Mesh Method ◽  
Adaptive Moving Mesh Method

AbstractThis paper extends the adaptive moving mesh method developed by Tang and Tang [36] to two-dimensional (2D) relativistic hydrodynamic (RHD) equations. The algorithm consists of two “independent” parts: the time evolution of the RHD equations and the (static) mesh iteration redistribution. In the first part, the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations. The second part is an iterative procedure. In each iteration, the mesh points are first redistributed, and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.

THE RESIDUAL-FREE BUBBLE NUMERICAL METHOD WITH QUADRATIC ELEMENTS

2004 ◽  
Vol 14 (05) ◽  
pp. 641-661 ◽  
Author(s):  
M. I. ASENSIO ◽  
A. RUSSO ◽  
G. SANGALLI
Keyword(s):  
Error Analysis ◽  
Numerical Method ◽  
A Priori ◽  
General Context ◽  
Practical Implementation ◽  
Linear Diffusion ◽  
Numerical Tests ◽  
A Priori Error Analysis ◽  
Reaction Problem

In this paper we analyze the Residual-Free Bubble (RFB) method applied to the linear diffusion–advection–reaction problem. We propose a new a priori error analysis for the method and for its practical implementation in a quite general context, which allows, e.g. linear or quadratic elements on the resolvable scales. We also perform some numerical tests, showing in both cases the advantages of the method.

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