Finite-difference method for the Gamma equation on non-uniform grids

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Le Minh Hieu Truong Thi Hieu Hanh Dang Ngoc Hoang Thanh

Abstract

We propose a new monotone finite-difference scheme for the second-order local approximation on a nonuniform grid that approximates the Dirichlet initial boundary value problem (IBVP) for the quasi-linear convection-diffusion equation with unbounded nonlinearity, namely, for the Gamma equation obtained by transformation of the nonlinear Black-Scholes equation into a quasilinear parabolic equation. Using the difference maximum principle, a two-sided estimate and an a priori estimate in the C-norm are obtained for the solution of the difference schemes that approximate this equation.

 

DOI: https://doi.org/10.31276/VJSTE.61(4).03-08

Article Details

How to Cite
HIEU, Le Minh; HANH, Truong Thi Hieu; THANH, Dang Ngoc Hoang. Finite-difference method for the Gamma equation on non-uniform grids. Vietnam Journal of Science, Technology and Engineering, [S.l.], v. 61, n. 4, p. 3-8, dec. 2019. ISSN 2525-2461. Available at: <http://vietnamscience.vjst.vn/index.php/VJSTE/article/view/259>. Date accessed: 06 apr. 2020.
Section
MATHEMATICS AND COMPUTER SCIENCE