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March  2003, 2(1): 91-99. doi: 10.3934/cpaa.2003.2.91

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, Hong Kong
2. 

Department of Statistics, Oxford University, 1 South Parks Road, Oxford, OX1 3TG, United Kingdom

Received  February 2002 Revised  November 2002 Published  December 2002

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.
Keywords: Two-way diffusions, integral equations., partial differential equations, forward-backward diffusions.
Mathematics Subject Classification: 60J60, 60J65, 60J70, 45E1.
Citation: G. Wei, P. Clifford. Analysis and numerical approximation of a class of two-way diffusions. Communications on Pure & Applied Analysis, 2003, 2 (1) : 91-99. doi: 10.3934/cpaa.2003.2.91
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