Series expansions of solutions of uxx + (2νx) ux + ε2utt = ut
Document Type
Article
Publication Date
2-1984
Department
Department of Mathematical Sciences; Department of Computer Science
Abstract
We investigate series expansions of solutions of the equation (*)uxx + 2νx-1ux + ε{lunate}2utt = ut, in terms of either a set of polynomial solutions for this equation or the associated functions for these polynomials. Our results extend those of Rosenbloom-Widder, Cholewinski-Haimo and the second author, who have previously studied (*) for various choices of the nonnegative parameters ν and ε. By considering (*) as a singular perturbation of the generalized heat equation (the ε = 0 case), we show that the polynomial solutions, associated functions and fundamental singularities of these equations are related by a basic integral transform.
Publication Title
Journal of Computational and Applied Mathematics
Recommended Citation
Givens, C.,
&
Chi Yeung Lo
(1984).
Series expansions of solutions of uxx + (2νx) ux + ε2utt = ut.
Journal of Computational and Applied Mathematics,
10(1), 7-23.
http://doi.org/10.1016/0377-0427(84)90064-5
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5692