This paper presents a boundary integral equation method with the adjoint generalized Neumann kernel for computing conformal mapping of unbounded multiply connected regions and its inverse onto several classes of canonical regions. For each canonical region, two integral equations are solved before one can approximate the boundary values of the mapping function. Cauchy's-type integrals are used for computing the mapping function and its inverse for interior points. This method also works for regions with piecewise smooth boundaries. Three examples are given to illustrate the effectiveness of the proposed method.

We present a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto five types of canonical slit regions. For each canonical region, 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 modified Neumann kernels and the adjoint generalized Neumann kernels.

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.

Dalam konteks penyebaran COVID-19, permodelan matematik telah menjadi satu komponen penting dalam merangka strategi bagi mengambil langkah awal dalam menangani penularan wabak. Dalam kajian ini, model SIR (“Susceptible” – “Infected” – “Removed”) digunakan bagi meramalkan tindak balas wabak COVID-19 di Malaysia. Menggunakan data rasmi daripada Kementerian Kesihatan Malaysia, didapati kes puncak Ketika PKP 1.0 berlaku pada t=21 hari (8 April 2020) dengan kadar jangkitan a = 0.19. Hasil kajian mendapati bahawa wujud perbezaan yang ketara sekiranya bilangan penduduk yang berpotensi dijangkiti S(0) dikurangkan, di mana puncak kes aktif dapat dikurangkan dengan begitu ketara (kes aktif puncak berlaku pada t=81, dengan peratusan kes berjumlah S(81) = 8.7%). Jadi, adalah amat penting bagi mematuhi arahan – arahan serta SOP yang digariskan oleh pihak kerajaan bagi menghentikan jangkitan pandemik COVID-19.