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

This paper derives sharp estimates of the error arising fromexplicit and implicit approximations of the constant-coefficient1D convection–diffusion equation with Dirac initial data.The error analysis is based on Fourier analysis and asymptoticapproximation of the integrals resulting from the inverse Fouriertransform. This research is motivated by applications in computationalfinance and the desire to prove convergence of approximationsto adjoint partial differential equations.