Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

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.

This paper presents a new approach to spectral methods for initial boundary value problems. A filtered version of the partial differential equation and the initial and boundary conditions at an ...