Fourier's well-known heat equation, introduced in 1822, describes how temperature changes in space and time when heat flows through a material. In general, this formulation works well to describe heat ...

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 ...

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 ...