In this paper, the elliptic partial differential equation is combined, and based on the high-resolution image processing technology, the effective ways to improve the quality of online video courses ...

Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards ...

Abstract: In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane ...

Boundary value problems for nonlinear partial differential equations form a cornerstone of modern mathematical analysis, bridging theoretical advancements and practical real-world applications. These ...

Abstract: The Lie algebraic method provides an important research direction for nonlinear filtering theory. By interpreting the Duncan-Mortensen-Zakai equation or its robust form as a partial ...

The fractional-order nonlinear Gardner and Cahn–Hilliard equations are often used to model ultra-short burst beams of light, complex fields of optics, photonic transmission systems, ions, and other ...

1 Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt 2 Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt This paper investigates the ...

This module introduces you to the theory of Partial Differential Equations (PDEs) studying in detail the three fundamental linear PDEs of second-order: the Laplace equation, the heat equation, and the ...