Finite-difference method for the Gamma equation on non-uniform grids
Keywords:Gamma equation, maximum principle, monotone finite-difference scheme, non-uniform grid, quasi-linear parabolic equation, scientific computing, two-side estimates
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.
Received 1 August 2019; accepted 11 November 2019
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