Communications on Pure and Applied Analysis (CPAA)

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

Pages: 91 - 99, Volume 2, Issue 1, March 2003      doi:10.3934/cpaa.2003.2.91

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G. Wei - Department of Mathematics, Hong Kong Baptist University, Hong Kong (email)
P. Clifford - Department of Statistics, Oxford University, 1 South Parks Road, Oxford, OX1 3TG, United Kingdom (email)

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.

Keywords:  Two-way diffusions, forward-backward diffusions, partial differential equations, integral equations.
Mathematics Subject Classification:  60J60, 60J65, 60J70, 45E10.

Received: February 2002;      Revised: November 2002;      Available Online: December 2002.