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 ...

Almost periodic functions serve as a powerful conceptual framework in analysing differential equations whose coefficients or forcing terms exhibit recurrent behaviour over time. Rooted in the ...

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...

Initial value problems for first order partial functional almost linear equations with unbounded delay are considered. The functional dependence is represented by the generalized Hale operator with ...

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 ...

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 ...

Vector analysis; matrices and determinants; theory of analytical functions; differential equations, Fourier series, Laplace transforms, distributions, Fourier transforms. Students taking ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...