Abstract
This paper presents a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto circular slit regions. Three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unbounded multiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the classical and the adjoint generalized Neumann kernels. Several numerical examples are presented.
Highlights
Conformal mapping is a special mapping that uses function of complex variable to transform a planar region onto another planar region while the angles between curves are preserved in magnitude as well as in their direction
With regards to conformal mapping, canonical region is known as a set of finitely connected regions S such that each finitely connected non-degenerate region is conformally equivalent to a region in S
Boundary integral equation related to a boundary relationship satisfied by a function which is analytic in a connected region interior to a closed smooth Jordan curve has been given by [4] and [5]
Summary
Conformal mapping is a special mapping that uses function of complex variable to transform a planar region onto another planar region while the angles between curves are preserved in magnitude as well as in their direction. Hu [6] and Murid and Hu [7] managed to construct a boundary integral equation for numerical conformal mapping of bounded multiply connected region onto a unit disk with slits. Sangawi et al [9] have constructed new linear boundary integral equations for conformal mapping of bounded multiply region onto a unit disk with circular slits, which improves the work of [7] and [4]. Yunus et al [10] managed to extent work by [4] and [9] for numerical conformal mapping of unbounded multiply connected region onto exterior unit disk with circular slits. Yunus et al / Malaysian Journal of Fundamental & Applied Sciences Vol., No.1 (2012) 38-43
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