Polynomial equations are fundamental concepts in mathematics that define relationships between numbers and variables in a structured manner. In mathematics, various equations are composed using ...

The theory of Appell polynomials has long intrigued researchers due to its elegant algebraic structure and rich connections with differential equations. At its core, an Appell sequence is ...

We consider solving integral equations on a piecewise smooth surface S in R3 with a smooth kernel function, using piecewise polynomial collocation interpolation of the surface. The theoretical ...

SIAM Journal on Numerical Analysis, Vol. 55, No. 1 (2017), pp. 63-86 (24 pages) A new space-time discontinuous Galerkin (dG) method utilizing special Trefftz polynomial basis functions is proposed and ...

Polyanalytic function theory extends the classical theory of holomorphic functions by encompassing functions that satisfy higher‐order generalisations of the Cauchy–Riemann equations. This broader ...