Search results for " numerical convergence"

showing 1 items of 1 documents

Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation

2004

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

Nonlinear systemDiscretizationDifferential equationConvergence (routing)Finite differenceCompact finite differenceApplied mathematicsBlack–Scholes modelViscosity solutionHigh-order compact finite differences numerical convergence viscosity solution financial derivativesMathematics
researchProduct