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 ...

A new definition of a guiding function for functional differential equations is given, which is sometimes better for applications than the known one by Mawhin. We then prove an existence result for ...

The closed-form solution of each of these general Cauchy-type problems is derived in terms of the function $ {\mathrm {\Phi }}_ {2}^ {\left (\mathrm {n}\right)}$ itself. Several special cases of the ...

In this paper, we define some non-elementary amplitude functions that are giving solutions to some well-known second-order nonlinear ODEs and the Lorenz equations, but not the chaos case. We are ...

This paper discusses the technique of “generating” certain analytically-defined mathematical functions by continuously solving a differential equation having the desired function as solution. This ...

Solutions of nonlinear partial differential equations can have enormous complexity, with nontrivial structure over a large range of length- and timescales. Developing effective theories that integrate ...

Abstract In a one-dimensional advection-diffusion equation with temporally dependent coefficients three cases may arise: solute dispersion parameter is time dependent while the flow domain ...