Convergence Rates of Moving Mesh Rannacher Methods for PDEs of Asian Options Pricing (Journal of Computational Mathematics, 2018)
This paper studies the convergence rates of a moving mesh implicit finite difference method with interpolation for partial differential equations (PDEs) with moving boundary arising in Asian option pricing. The moving mesh scheme is based on Rannacher time-stepping approach whose idea is running the implicit Euler schemes in the initial few steps and continuing with Crank-Nicolson schemes. With graded meshes for time direction and moving meshes for space direction, the fully discretized scheme is constructed using quadratic interpolation between two consecutive time level for the PDEs with moving boundary. The second-order convergence rates in both time and space are proved and numerical examples are carried out to confirm the theoretical results.