Using Chebyshev Polynomials to Approximate Partial Differential Equations
20 Pages Posted: 28 May 2008
Date Written: May 1, 2008
This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. It consists of determining the value function by using a set of nodes and basis functions. We provide two examples: pricing a European option and determining the best policy for shutting down a machine. The suggested method is flexible, easy to programme and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.
Keywords: European options, Chebyshev polynomial approximation, Chebyshev nodes
JEL Classification: C63, G12
Suggested Citation: Suggested Citation