Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.

Covers finite difference, finite element, finite volume, pseudo-spectral, and spectral methods for elliptic, parabolic, and hyperbolic partial differential equations. Prereq., APPM 5600. Recommended ...

Partial Differential Equations (PDEs) play a pivotal role in understanding numerous natural phenomena. These equations describe how quantities change over space and time, and they are vital in fields ...

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

1 Department of Mathematics, University of Education, Okara Campus, Okara, Pakistan. 2 Center for Undergraduate Studies, University of the Punjab, Lahore, Pakistan. 3 Air University Multan Campus, ...

Contributed by Thomas Y. Hou; received January 13, 2025; accepted May 20, 2025; reviewed by Russel E. Caflisch, Javier Gómez-Serrano, Vladimir Sverak, and Terence C. Tao This contribution is part of ...

Abstract: When planet bearing operates under a complex and variable environment, the fault signal is often coupled with signals from other transmission components and is influenced by the transmission ...