The operational matrices of two dimensional Bernstein polynomials for solving the hyperbolic partial differential equation with boundary conditions

	The operational matrices of two dimensional Bernstein polynomials for solving the hyperbolic partial differential equation with boundary conditions
International Journal of Nonlinear Analysis and Applications
مقاله 9، دوره 16، شماره 7، مهر 2025، صفحه 107-120 اصل مقاله (657.74 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.32159.4777
نویسندگان
Mohsen Mohamadi^* ؛ Amir Shahmari؛ Hassan Eshaghi Kenari
Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran
چکیده
The wave equations are one of the most important equations in engineering and physics, which are usually formulated as hyperbolic partial differential equations with special boundary conditions. In this paper, a numerical method for solving these equations based on Bernstein polynomials is introduced. The properties of Bernstein polynomial operational matrices turn this differential equation and its boundary conditions into a system of algebraic equations. Some numerical examples illustrate the accuracy, validity, and applicability of the new technique.
کلیدواژه‌ها
Bernstein polynomial؛ two dimensions Bernstein polynomial؛ Best approximation؛ Operational matrices؛ Kronecker products؛ Hyperbolic Partial differential equation of second order
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