A Technique to Solve a Parabolic Equation by Point Symmetries that Incorporate Initial Data

dc.contributor.authorJamal, Sameerah
dc.contributor.otherauthorMaphanga, Rivoningo
dc.date.accessioned2025-03-19T12:13:45Z
dc.date.issued2025-03
dc.description.abstractIn this paper, we show how transformation techniques coupled with a convolution integral can be used to solve a generalised option-pricing model, including the Black–Scholes model. Such equations are parabolic and the special convolutions are extremely involved as they arise from an initial value problem. New symmetries are derived to obtain solutions through an application of the invariant surface condition. The main outcome is that the point symmetries are effective in producing exact solutions that satisfy a given initial condition, such as those represented by a call-option.
dc.description.submitterPM2025
dc.facultyFaculty of Science
dc.identifier0000-0003-3702-8368
dc.identifier.citationJamal, S., Maphanga, R. A Technique to Solve a Parabolic Equation by Point Symmetries that Incorporate Initial Data. Int. J. Appl. Comput. Math 11, 48 (2025). https://doi.org/10.1007/s40819-025-01861-6
dc.identifier.issn2349-5103 (print)
dc.identifier.issn2199-5796 (online)
dc.identifier.other10.1007/s40819-025-01861-6
dc.identifier.urihttps://hdl.handle.net/10539/44392
dc.journal.titleInternational Journal of ComputationaI Mathematics
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofseriesVol. 11; No. 48
dc.rights© The Author(s) 2025. Open Access, This article is licensed under a Creative Commons Attribution 4.0 International License.
dc.schoolSchool of Mathematics
dc.subjectOption-pricing
dc.subjectSymmetries
dc.subjectHeat transfer
dc.subjectInitial conditions
dc.subjectPricing equation
dc.subject.primarysdgSDG-17: Partnerships for the goals
dc.titleA Technique to Solve a Parabolic Equation by Point Symmetries that Incorporate Initial Data
dc.typeArticle

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