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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- Dangl, Thomas & Wirl, Franz, 2004. "Investment under uncertainty: calculating the value function when the Bellman equation cannot be solved analytically," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1437-1460, April.
- Niko Jaakkola, 2013. "Green Technologies and the Protracted End to the Age of Oil: A strategic analysis," OxCarre Working Papers 099, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
- Alejandro Mosiño, 2012. "Using Chebyshev Polynomials to Approximate Partial Differential Equations: A Reply," Computational Economics, Society for Computational Economics, vol. 39(1), pages 13-27, January.
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