On the Derivation of Nonclassical Symmetries of the Black–Scholes Equation via an Equivalence Transformation
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-12-28
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
The nonclassical symmetries method is a powerful extension of the classical symmetries method for finding exact solutions of differential equations.
Through this method, one is able to arrive at new exact solutions of a given differential equation, i.e., solutions that are not obtainable directly as invariant solutions from classical symmetries of the equation.
The challenge with the nonclassical symmetries method, however, is that governing equations for the admitted nonclassical symmetries are typically coupled and nonlinear and therefore difficult to solve.
In instances where a given equation is related to a simpler one via an equivalent transformation, we propose that nonclassical symmetries of the given equation may be obtained by transforming nonclassical symmetries of the simpler equation using the equivalence transformation.
This is what we illustrate in this paper.
We construct four nontrivial nonclassical symmetries of the Black–Scholes equation by transforming nonclassical symmetries of the heat equation.
For completeness, we also construct invariant solutions of the Black–Scholes equation associated with the determined nonclassical symmetries.
American Psychological Association (APA)
Sinkala, Winter. 2020. On the Derivation of Nonclassical Symmetries of the Black–Scholes Equation via an Equivalence Transformation. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-7.
https://search.emarefa.net/detail/BIM-1197048
Modern Language Association (MLA)
Sinkala, Winter. On the Derivation of Nonclassical Symmetries of the Black–Scholes Equation via an Equivalence Transformation. Mathematical Problems in Engineering No. 2020 (2020), pp.1-7.
https://search.emarefa.net/detail/BIM-1197048
American Medical Association (AMA)
Sinkala, Winter. On the Derivation of Nonclassical Symmetries of the Black–Scholes Equation via an Equivalence Transformation. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-7.
https://search.emarefa.net/detail/BIM-1197048
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1197048