Boundary Integral Equations with the Generalized Neumann kernel for Robin problem in Simply Connected Region
A mixed boundary value problem with the linear combination of Dirichlet and Neumann conditions is called a Robin problem. In this paper, we consider the Robin problem in a bounded simply connected region with smooth boundary It consists of finding a function u harmonic in and satisfies the Robin boundary condition. This work develops new boundary integral equations for solving the Robin problem. Recently, the interplay of Riemann-Hilbert problems (briefly, RH problems) with conformal mapping, Dirichlet problem and Neumann problem has been studied extensively. The related integral equations involving the generalized Neumann kernel are uniquely solvable. In this paper we show how to reformulate a Robin problem as a Riemann-Hilbert problem. Numerical results are presented to illustrate the solution technique for the Robin problem when the boundaries are sufficiently smooth.
Disclaimer/Regarding indexing issue:
We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.