A Novel Approach to Calculating the Riemann Mapping Function Using Real-Valued Kernels

Section: Articles
Issue
Vol. 20 No. 1 (2026): Vol. 20 No. 1 (2026): Volume 20 Issue 1
Pages
69-74

Keywords:

Nyström method, Interior mapping function, Kerzman-Stein Trummer, Boundary integral equations, Riemann Mapping

Abstract

This paper discusses the general boundary integral equations, Riemann mapping function for bounded simply connected regions whose boundary curves are smooth and analytic, that correspond to a real-valued kernel, and a new boundary integral formula is introduced. Based on the multiplication of the Kerzman-Stien Trummer integral formula (briefly, KSTiF) by the penalty function, such that the complex-valued kernel transforms into, we derive a new formula and prove its uniqueness. Numerical results using the Nyström method with the trapezoidal rule yield approximations of high accuracy when compared with exact solutions for test regions.  

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Author

Shwan Alshatri

Rozh Preparatory School, Sulaymaniyah, 46001, Kurdistan Region- Iraq

Identifiers

DOI: 10.33899/rjcsm.v20i1.60666

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A Novel Approach to Calculating the Riemann Mapping Function Using Real-Valued Kernels. (2026). AL-Rafidain Journal of Computer Sciences and Mathematics, 20(1), 69-74. https://doi.org/10.33899/rjcsm.v20i1.60666
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How to Cite

A Novel Approach to Calculating the Riemann Mapping Function Using Real-Valued Kernels. (2026). AL-Rafidain Journal of Computer Sciences and Mathematics, 20(1), 69-74. https://doi.org/10.33899/rjcsm.v20i1.60666