Uniform convergence analysis of an upwind finite-difference approximation of a convection-diffusion boundary value problem on an adaptive grid

1999 ◽  
Vol 19 (2) ◽  
pp. 233-249 ◽  
Author(s):  
J Mackenzie
Keyword(s):  
Finite Difference ◽  
Boundary Value Problem ◽  
Uniform Convergence ◽  
Convergence Analysis ◽  
Adaptive Grid ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Diffusion Boundary ◽  
Convection Diffusion ◽  
Upwind Finite Difference

Bifurcation of Homoclinic Structures: I. Finite Difference Approximation and Mechanisms for Spurious Solutions

1997 ◽  
Vol 07 (02) ◽  
pp. 287-317
Author(s):  
Jürgen Gerling ◽  
Hartmut Jürgens ◽  
Heinz-Otto Peitgen
Keyword(s):  
Dynamical System ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Discrete Dynamical System ◽  
Finite Difference Approximation ◽  
Nonlinear Boundary Value Problem ◽  
Difference Approximation ◽  
Spurious Solutions

In the present paper we consider the finite difference approximation for a specific nonlinear boundary value problem which generates spurious solutions. Several mechanisms for spurious solutions will be presented. The key connection is that of the homoclinic structure of an adjoint time discrete dynamical system.

Wavelet-optimized compact finite difference method for convection–diffusion equations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mani Mehra ◽  
Kuldip Singh Patel ◽  
Ankita Shukla
Keyword(s):  
Finite Difference ◽  
Two Dimensions ◽  
Finite Difference Approximation ◽  
Diffusion Equations ◽  
Difference Approximation ◽  
Uniform Grid ◽  
Adaptive Grids ◽  
Smooth Functions ◽  
Compact Finite Difference ◽  
Convection Diffusion

AbstractIn this article, compact finite difference approximations for first and second derivatives on the non-uniform grid are discussed. The construction of diffusion wavelets using compact finite difference approximation is presented. Adaptive grids are obtained for non-smooth functions in one and two dimensions using diffusion wavelets. High-order accurate wavelet-optimized compact finite difference (WOCFD) method is developed to solve convection–diffusion equations in one and two dimensions on an adaptive grid. As an application in option pricing, the solution of Black–Scholes partial differential equation (PDE) for pricing barrier options is obtained using the proposed WOCFD method. Numerical illustrations are presented to explain the nature of adaptive grids for each case.

Bifurcation of Homoclinic Structures.

1997 ◽  
Vol 07 (03) ◽  
pp. 527-549
Author(s):  
Jürgen Gerling ◽  
Hartmut Jürgens ◽  
Heinz-Otto Peitgen
Keyword(s):  
Finite Elements ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Periodic Structure ◽  
Nonlinear Boundary ◽  
Specific Area ◽  
Finite Difference Approximation ◽  
Approximation Schemes ◽  
Difference Approximation ◽  
Area Preserving

This paper is a continuation of Gerling et al. [1997] and investigates the periodic structure of a specific area-preserving homeomorphism which is generated by the finite difference approximation for a nonlinear boundary value problem. Moreover, these and prior results are extended to further approximation schemes like collocation and finite elements.

scholarly journals Finite Difference Approximation Method for a Space Fractional Convection–Diffusion Equation with Variable Coefficients

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 485 ◽  
Author(s):  
Eyaya Fekadie Anley ◽  
Zhoushun Zheng
Keyword(s):  
Finite Difference ◽  
Variable Coefficients ◽  
Convective Transport ◽  
Transport Processes ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Convection Diffusion ◽  
Integer Order ◽  
Difference Formula ◽  
The Right

Space non-integer order convection–diffusion descriptions are generalized form of integer order convection–diffusion problems expressing super diffusive and convective transport processes. In this article, we propose finite difference approximation for space fractional convection–diffusion model having space variable coefficients on the given bounded domain over time and space. It is shown that the Crank–Nicolson difference scheme based on the right shifted Grünwald–Letnikov difference formula is unconditionally stable and it is also of second order consistency both in temporal and spatial terms with extrapolation to the limit approach. Numerical experiments are tested to verify the efficiency of our theoretical analysis and confirm order of convergence.

Sign in / Sign up

Export Citation Format

Share Document