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

Journal article

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.

Authors: Carter, R; Giles, M

• Publication status: Published
• Journal: IMA JOURNAL OF NUMERICAL ANALYSIS
• Volume: 27
• Issue: 2
• Pages: 406-425
• Publication date: 2007-04-01
• DOI: 10.1093/imanum/drl043
• EISSN: 1464-3642
• ISSN: 0272-4979
• Language: English
• Keywords: Crank-Nicolson time marching; Dirac initial data; Rannacher startup; convection-diffusion equation