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A higher order orthogonal collocation technique for discontinuous two dimensional problems with Neumann boundary conditions | ||
Computational Methods for Differential Equations | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 مهر 1403 اصل مقاله (1.16 M) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22034/cmde.2024.60344.2577 | ||
نویسندگان | ||
Santosh Kumar Bhal1؛ Ashish Kumar Nandi* 2؛ Abedallah Rababah3 | ||
1Department of Mathematics, School of Advanced Sciences and Languages, Vellore Institute of Technology, Bhopal, India. | ||
2Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu-600127, India. | ||
3Department of Mathematical Sciences, United Arab Emirates University, United Arab Emirates. | ||
چکیده | ||
In this paper, the orthogonal spline collocation method (OSCM) is employed to address the solution of the Helmholtz equation in two-dimensional problems. It is characterized by discontinuous coefficients with certain wave numbers. The solution is approximated by employing distinct basis functions namely, monomial along the x-direction and Hermite along the y-direction. Additionally, to solve the two-dimensional problems efficiently in the sense of computational cost with less operation counts, matrix decomposition algorithm (MDA) is used to convert it into a set of one-dimensional problems. As a consequence, the resulting reduced matrix becomes non-singular in discrete cases. To assess the performance of the proposed numerical scheme, a grid refinement analysis is conducted to incorporate various wave coefficients of the Helmholtz equation. The illustrations and examples demonstrate a higher order of convergence compared to existing methods. | ||
کلیدواژهها | ||
Helmholtz equation؛ Monomial basis functions؛ Orthogonal spline collocation methods (OSCM)؛ Generalized eigenvalue problem؛ Matrix decomposition algorithm (MDA) | ||
آمار تعداد مشاهده مقاله: 26 تعداد دریافت فایل اصل مقاله: 58 |