TITLE:
Approximate Solutions to the Discontinuous Riemann-Hilbert Problem of Elliptic Systems of First Order Complex Equations
AUTHORS:
Guochun Wen, Yanhui Zhang, Dechang Chen
KEYWORDS:
Discontinuous Riemann-Hilbert Problem, Elliptic Systems of First Order Complex Equations, Esti-mates and Existence of Solutions, Multiply Connected Domains
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.10,
June
6,
2014
ABSTRACT: Several
approximate methods have been used to find approximate solutions of elliptic
systems of first order equations. One common method is the Newton imbedding
approach, i.e. the parameter
extension method. In this article, we discuss approximate solutions to
discontinuous Riemann-Hilbert boundary value problems, which have various
applications in mechanics and physics. We first formulate the discontinuous
Riemann-Hilbert problem for elliptic systems of first order complex equations
in multiply connected domains and its modified well-posedness, then use the parameter
extensional method to find approximate solutions to the modified boundary value
problem for elliptic complex systems of first order equations, and then provide
the error estimate of approximate solutions for the discontinuous boundary
value problem.