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Bhal, Santosh, Nandi, Ashish, Rababah, Abedallah. (1403). A higher order orthogonal collocation technique for discontinuous two dimensional problems with Neumann boundary conditions. سامانه مدیریت نشریات علمی, (), -. doi: 10.22034/cmde.2024.60344.2577
Santosh Kumar Bhal; Ashish Kumar Nandi; Abedallah Rababah. "A higher order orthogonal collocation technique for discontinuous two dimensional problems with Neumann boundary conditions". سامانه مدیریت نشریات علمی, , , 1403, -. doi: 10.22034/cmde.2024.60344.2577
Bhal, Santosh, Nandi, Ashish, Rababah, Abedallah. (1403). 'A higher order orthogonal collocation technique for discontinuous two dimensional problems with Neumann boundary conditions', سامانه مدیریت نشریات علمی, (), pp. -. doi: 10.22034/cmde.2024.60344.2577
Bhal, Santosh, Nandi, Ashish, Rababah, Abedallah. A higher order orthogonal collocation technique for discontinuous two dimensional problems with Neumann boundary conditions. سامانه مدیریت نشریات علمی, 1403; (): -. doi: 10.22034/cmde.2024.60344.2577

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)
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