Mathematics 2014, 2(2), 96-118; doi:10.3390/math2020096

The Riccati System and a Diffusion-Type Equation

1,2,* email, 1email and 3email
Received: 31 December 2013; in revised form: 27 February 2014 / Accepted: 14 April 2014 / Published: 15 May 2014
(This article belongs to the Special Issue Mathematics on Partial Differential Equations)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: We discuss a method of constructing solutions of the initial value problem for diffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is also considered. Examples include, but are not limited to the Fokker-Planck equation in physics, the Black-Scholes equation and the Hull-White model in finance.
Keywords: diffusion-type equations; Green’s function; fundamental solution; autonomous and nonautonomous Burgers equations; Fokker-Planck equation; Black-Scholes equation; the Hull-White model; Riccati equation and Riccati-type system; Ermakov equation and Ermakov-type system
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MDPI and ACS Style

Suazo, E.; Suslov, S.K.; Vega-Guzmán, J.M. The Riccati System and a Diffusion-Type Equation. Mathematics 2014, 2, 96-118.

AMA Style

Suazo E, Suslov SK, Vega-Guzmán JM. The Riccati System and a Diffusion-Type Equation. Mathematics. 2014; 2(2):96-118.

Chicago/Turabian Style

Suazo, Erwin; Suslov, Sergei K.; Vega-Guzmán, José M. 2014. "The Riccati System and a Diffusion-Type Equation." Mathematics 2, no. 2: 96-118.

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