Mickens, Ronald E.; Munyakazi, Justin; Washington, Talitha M. A note on the exact discretization for a Cauchy-Euler equation: application to the Black-Scholes equation. (English) Zbl 1326.65095 J. Difference Equ. Appl. 21, No. 7, 547-552 (2015). Summary: We construct the exact finite difference representation for a second-order, linear, Cauchy-Euler ordinary differential equation. This result is then used to construct new non-standard finite difference schemes for the Black-Scholes partial differential equation. Cited in 3 Documents MSC: 65L12 Finite difference and finite volume methods for ordinary differential equations 34A30 Linear ordinary differential equations and systems 65L05 Numerical methods for initial value problems involving ordinary differential equations 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 35Q91 PDEs in connection with game theory, economics, social and behavioral sciences 91G60 Numerical methods (including Monte Carlo methods) Keywords:Cauchy-Euler equation; exact finite difference schemes; Black-Scholes equation; sub-equations PDFBibTeX XMLCite \textit{R. E. Mickens} et al., J. Difference Equ. Appl. 21, No. 7, 547--552 (2015; Zbl 1326.65095) Full Text: DOI References: [1] DOI: 10.1086/260062 · Zbl 1092.91524 · doi:10.1086/260062 [2] DOI: 10.2307/3003143 · doi:10.2307/3003143 [3] R.E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific, River Edge, NJ, 1994. · Zbl 0810.65083 [4] DOI: 10.1080/1023619021000000807 · doi:10.1080/1023619021000000807 [5] DOI: 10.2307/2321656 · Zbl 0498.34049 · doi:10.2307/2321656 [6] S.L. Ross, Differential Equations, Blairdell, Waltham, MA, 1964. [7] DOI: 10.1080/10236198.2013.771635 · Zbl 1300.65055 · doi:10.1080/10236198.2013.771635 [8] P. Wilmott, S. Howison, and J. Dewynne, The Mathematics of Financial Derivatives, Cambridge University Press, New York, 2002. · Zbl 0842.90008 [9] P. Wilmott, Paul Wilmott on Quantitative Finance, Vols. 1 and 2, Wiley, Chichester, 2000. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.