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.