Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

Heun functions, which generalise the well‐known hypergeometric functions, are solutions to the Heun differential equation – a second‐order linear differential equation with four regular singular ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

The paper presents a variant of implicit function theorem, as a corollary of existence theorem for solutions of a first order system of partial differential equations. This results is then extend to ...