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

Authors

  • Le Minh Hieu* University of Economics, The University of Danang
  • Truong Thi Hieu Hanh University of Economics, The University of Danang
  • Dang Ngoc Hoang Thanh Hue College of Industry

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.

Keywords:

Gamma equation, maximum principle, monotone finite-difference scheme, non-uniform grid, quasi-linear parabolic equation, scientific computing, two-side estimates

DOI:

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

Classification number

1.1

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Published

2019-12-15

Received 1 August 2019; accepted 11 November 2019

How to Cite

Le Minh Hieu, Truong Thi Hieu Hanh, & Dang Ngoc Hoang Thanh. (2019). Finite-difference method for the Gamma equation on non-uniform grids. Vietnam Journal of Science, Technology and Engineering, 61(4), 3-8. https://doi.org/10.31276/VJSTE.61(4).03-08

Issue

Vol. 61 No. 4 (2019)

Section

Mathematics and Computer Science

License

This work is licensed under a Attribution-NonCommercial-NoDerivatives 4.0 International