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Extension of Euler's method to parabolic equations
Ansvarig organisation
2009 (Engelska)Ingår i: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 14, nr 4, s. 1157-1168Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

Euler generalized d'Alembert's solution to a wide class of linear hyperbolic equations with two independent variables. He introduced in 1769 the quantities that were rediscovered by Laplace in 1773 and became known as the Laplace invariants. The present paper is devoted to an extension of Euler's method to linear parabolic equations with two independent variables. The new method allows one to derive an explicit formula for the general solution of a wide class of parabolic equations. In particular, the general solution of the Black-Scholes equation is obtained. (c) 2008 Elsevier B.V. All rights reserved.

Ort, förlag, år, upplaga, sidor
AMSTERDAM: ELSEVIER SCIENCE BV , 2009. Vol. 14, nr 4, s. 1157-1168
Nyckelord [en]
Parabolic equations, Semi-invariant, Reducible equations, General solution to Black-Scholes equation
Nationell ämneskategori
Matematisk analys Matematik
Identifikatorer
URN: urn:nbn:se:bth-8172DOI: 10.1016/j.cnsns.2008.04.010ISI: 000264295800024Lokalt ID: oai:bth.se:forskinfo9C7D70EF73F96514C12575B00020EC77OAI: oai:DiVA.org:bth-8172DiVA, id: diva2:835861
Tillgänglig från: 2012-09-18 Skapad: 2009-05-08 Senast uppdaterad: 2017-12-04Bibliografiskt granskad

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