The Riccati system and a diffusion-type equation (Q401969)
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scientific article; zbMATH DE number 6334888
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Riccati system and a diffusion-type equation |
scientific article; zbMATH DE number 6334888 |
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The Riccati system and a diffusion-type equation (English)
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27 August 2014
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Summary: 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.
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autonomous and nonautonomous Burgers equations
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Black-Scholes equation
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Hull-White model
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Riccati equation and Riccati-type system
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Ermakov equation and Ermakov-type system
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