Analysis and numerical approximation of a class of two-way diffusions

G. Wei; P. Clifford

doi:10.3934/cpaa.2003.2.91

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2003, Volume 2, Issue 1: 91-99. Doi: 10.3934/cpaa.2003.2.91

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Analysis and numerical approximation of a class of two-way diffusions

G. Wei^1, and
P. Clifford^2,

1.
Department of Mathematics, Hong Kong Baptist University
2.
Department of Statistics, Oxford University, 1 South Parks Road, Oxford, OX1 3TG

Received: February 2002

Revised: November 2002

Published: November 2003

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Abstract

We consider a class of two-way diffusions with reflecting boundary conditions. We show that the problem can be reduced to the investigation of the solution of an Abel integral equation and the solution of two classical one-way diffusion problems. We approximate the solution of the integral equation by the product of a piecewise constant function and the known solution of the problem with infinite boundaries. A numerical solution of high accuracy is then obtained by solving a stable linear system.

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Mathematics Subject Classification: 60J60, 60J65, 60J70, 45E10.

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