Author/Authors :
Nazar, Kashif Universiti Teknologi Malaysia (UTM) - Faculty of Science - Department of Mathematical Sciences, Malaysia , Nazar, Kashif COMSATS Institute of Information Technology - Department of Mathematics, Pakistan , Murid, Ali H. M. Universiti Teknologi Malaysia (UTM) - Faculty of Science, UTM Centre for Industrial and Applied Mathematics (UTM‐CIAM) - Department of Mathematical Sciences, Malaysia , Sangawi, Ali W. K. Universiti Teknologi Malaysia (UTM) - UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Malaysia , Sangawi, Ali W. K. University of Sulaimani - School of Science, Faculty of Science and Science Education - Department of Mathematics, Iraq
Abstract :
This paper presents a new boundary integral equation with the adjoint Neumann kernel associated with θ,where θ is the boundary correspondence function of Ahlfors map of a bounded multiply connected region onto a unit disk. The proposed boundary integral equation is constructed from a boundary relationship satisfied by the Ahlfors map of a multiply connected region. The integral equation is solved numerically for θ, using combination of Nystrom method, GMRES method, and fast multiple method. From the computed values of θ,we solve for the boundary correspondence function θ which then gives the Ahlfors map. The numerical examples presented here prove the effectiveness of the proposed method.
Keywords :
Ahlfors map , adjoint Neumann kernel , Generalized Neumann kernel , GMRES , fast multipolemethod
