Chebyshev polynomial approximation to approximate partial differential equations

Provided by Research Papers in Economics

CHEBYSHEV POLYNOMIAL APPROXIMATION TO
APPROXIMATE PARTIAL DIFFERENTIAL EQUATIONS

Guglielmo Maria Caporale

Brunel University and London Metropolitan University

Mario Cerrato

University of Glasgow

March 2008

Abstract

This pa per suggests a simple method based on Chebyshev approximation at Chebyshev
nodes to approximate partial differential equations. The methodology simply consists in
determining the value function by using a set of nodes and basis functions. We provide
two examples. Pricing an European option and determining the best policy for chatting
down a machinery. The suggested method is flexible, easy to program and efficient. It is
also applicable in other fields, providing efficient solutions to complex systems of partial
differential equations.

JEL Classification: C63, G12

Keywords: European Options, Chebyshev Polynomial Approximation, Chebyshev Nodes

Corresponding author: Professor Guglielmo Maria Caporale, Brunel Business School,
Brunel University, Uxbridge, Middlesex UB8 3PH, UK. Tel.: +44 (0)1895 266713. Fax:
+44 (0)1895 269770. Email: [email protected]

Acknowledgements: We are grateful to Karim Abadir, Paresh Date, Brian Eales, and
Geoff Rodgers for useful comments and suggestions. The usual disclaimer applies.

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