Using Chebyshev Polynomials to Approximate Partial Differential Equations
AbstractThis 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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Bibliographic InfoArticle provided by Society for Computational Economics in its journal Computational Economics.
Volume (Year): 35 (2010)
Issue (Month): 3 (March)
European options; Chebyshev polynomial approximation; Chebyshev nodes; C63; G12;
Other versions of this item:
- Guglielmo Maria Caporale & Mario Cerrato, 2008. "Using Chebyshev Polynomials to Approximate Partial Differential Equations," CESifo Working Paper Series 2308, CESifo Group Munich.
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
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