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Chebyshev polynomial approximation to approximate partial differential equations

By Guglielmo Maria Caporale and Mario Cerrato

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.European Options, Chebyshev Polynomial Approximation, Chebyshev Nodes

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