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Bhal, Santosh, Nandi, Ashish, Rababah, Abedallah. (1404). A higher-order orthogonal collocation technique for discontinuous two-dimensional problems with Neumann boundary conditions. سامانه مدیریت نشریات علمی, 13(4), 1385-1399. 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, 13, 4, 1404, 1385-1399. doi: 10.22034/cmde.2024.60344.2577
Bhal, Santosh, Nandi, Ashish, Rababah, Abedallah. (1404). 'A higher-order orthogonal collocation technique for discontinuous two-dimensional problems with Neumann boundary conditions', سامانه مدیریت نشریات علمی, 13(4), pp. 1385-1399. 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, 1404; 13(4): 1385-1399. 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
مقاله 22، دوره 13، شماره 4، دی 2025، صفحه 1385-1399    اصل مقاله (449.81 K)
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 fewer operation counts, the matrix decomposition algorithm (MDA) is used to convert them 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؛ Orthogonal spline collocation methods؛ Matrix decomposition algorithm
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