Extension of Euler's method to parabolic equations
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences2009 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, Vol. 14, no 4, 1157-1168 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
AMSTERDAM: ELSEVIER SCIENCE BV , 2009. Vol. 14, no 4, 1157-1168 p.
Parabolic equations, Semi-invariant, Reducible equations, General solution to Black-Scholes equation
Mathematical Analysis Mathematics
IdentifiersURN: urn:nbn:se:bth-8172DOI: 10.1016/j.cnsns.2008.04.010ISI: 000264295800024Local ID: oai:bth.se:forskinfo9C7D70EF73F96514C12575B00020EC77OAI: oai:DiVA.org:bth-8172DiVA: diva2:835861