WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
Oleinik Line Method and Its Application
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Abstract: The paper studies the existence of the solution to the equation θηηw+wθξw−θtw=f(η,ξ,t,w). The equation comes from mathematics finance. With the help of Fichera-Oleinik theory, we find the suitable boundary value conditions to assure the posedness of the equation. By modifying Oleinik’s line method, we translate the mathematics finance equation to a system of ordinary differential equations, then by the uniformly estimates of the solution of the system, using Arzela Theorem, we can extract a convergent subsequence, which is convergent to the solution of the mathematics finance equation itself. Some constraint conditions of known functions f, w0, w1 and w2, that appearing in the initial boundary value conditions, are imposed.
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Keywords: Mathematics finance, Oleinik’s line method, Fichera-Oleinik theory, boundary condition, t-global solution
Pages: 768-779
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #75