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Caporale, Guglielmo Maria and Cerrato, Mario (2008) Using Chebyshev polynomials to approximate partial differential equations. Centre for International Capital Markets discussion papers, 2008 (10). pp. 1-15. ISSN 1749-3412
This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. It consists in 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.
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