Inverse problems in the context of elliptic equations and boundary value problems represent a critical area of mathematical analysis with wide-ranging applications in imaging, geophysics, and medical ...

Difference equations, as discrete analogues of differential equations, form a fundamental mathematical framework for describing systems that evolve incrementally over time or space. Coupled with ...

This monthly journal, published since 1900, is devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American ...

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

Fourier series solutions are obtained for mixed boundary value problems for the Laplace equation in the plane and in the sphere. The nature of the boundary conditions presents difficulties in ...