Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

The Helmholtz equation, a cornerstone in mathematical physics, models wave propagation phenomena in acoustics, electromagnetism and seismic imaging. Its inherent computational challenges—particularly ...

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. The system is consistent with the usual model for incompressible miscible displacement. Two ...

Nyström's method with the trapezoidal rule, and the Fourier method, produce the same approximation to the solution of an integral equation at the collocation points ...