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Convergence analysis of Crank-Nicolson and Rannacher time-marching

Abstract:

This paper presents a convergence analysis of Crank-Nicolson and Rannacher time-marching methods which are often used in finite difference discretisations of the Black-Scholes equations. Particular attention is paid to the important role of Rannacher's startup procedure, in which one or more initial timesteps use Backward Euler timestepping, to achieve second order convergence for approximations of the first and second derivatives. Numerical results confirm the sharpness of the error analysis...

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Publication date:
2005-08-05
URN:
uuid:e17ca056-6f7b-4e71-b4cd-a784805f4cf9
Local pid:
oai:eprints.maths.ox.ac.uk:1137

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