6533b7d7fe1ef96bd12678fb

RESEARCH PRODUCT

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

Michel FourniéAnsgar JüngelBertram Düring

subject

Matrix difference equationFTCS schemeNumerical AnalysisPartial differential equationApplied MathematicsMathematical analysisCompact finite differenceNumerical solution of the convection–diffusion equationFinite difference coefficientCentral differencing schemeComputational MathematicsModeling and SimulationAnalysisCompact convergenceMathematics

description

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.

yearjournalcountryeditionlanguage
2004-03-01ESAIM: Mathematical Modelling and Numerical Analysis
https://doi.org/10.1051/m2an:2004018