Wavelet-optimized compact finite difference method for convection–diffusion equations-Reference-Cited by-同舟云学术

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

Published:2020-12-04 Issue:3-4 Volume:22 Page:353-372
ISSN:1565-1339
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Mehra Mani¹^ORCID,Patel Kuldip Singh²,Shukla Ankita¹

Affiliation:

1. Indian Institute of Technology Delhi , New Delhi , India

2. Dr. SPM International Institute of Information Technology Naya Raipur , Naya Raipur , Chhattisgarh , India

Abstract

Abstract In 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.

Funder

Department of Science and Technology

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2018-0295/pdf

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