Sharp error estimates for discretizations of the 1D convection–diffusion equation with Dirac initial data

Abstract

This paper derives sharp estimates of the error arising from explicit and implicit approximations of the constant-coefficient 1D convection‐diffusion equation with Dirac initial data. The error analysis is based on Fourier analysis and asymptotic approximation of the integrals resulting from the inverse Fourier transform. This research is motivated by applications in computational finance and the desire to prove convergence of approximations to adjoint partial differential equations.