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Wavelet-optimized Compact Finite Difference Method for Convection–diffusion Equations by Mani Mehra; Kuldip Singh Patel; Ankita Shukla is a Mathematics article available to read on EtoBox.

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## 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.

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Author

Mani Mehra; Kuldip Singh Patel; Ankita Shukla

Publisher

Walter de Gruyter GmbH

Published

2020

Language

EN

Field

Mathematics (Physical Sciences)