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.

We study finite element methods for the wave equation in a rectangular domain with a second-order absorbing boundary condition imposed on the boundary. For this problem there seems to be no known ...

The initial boundary-value problem for the Korteweg-de Vries (KdV) equation on the negative quarter-plane, x < 0 and t > 0, is considered. The formulation of this problem is different to the usual ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...

Boundary value problems and integro-differential equations lie at the heart of modern applied mathematics, providing robust frameworks to model phenomena across physics, engineering and beyond. These ...