3 papers
math.NA2023
Asymptotic expansions for the linear PDEs with oscillatory input terms; Analytical form and error analysis
Karolina Kropielnicka, Rafał Perczyński
Partial differential equations with highly oscillatory input terms are hardly ever solvable analytically and their numerical treatment is difficult. Modulated Fourier expansion use…
math.NA2023
Numerical integrator for highly oscillatory differential equations based on the Neumann series
Rafał Perczyński, Grzegorz Madejski
We propose a third-order numerical integrator based on the Neumann series and the Filon quadrature, designed mainly for highly oscillatory partial differential equations. The metho…
math.NA2023
Asymptotic expansions for the solution of a linear PDE with a multifrequency highly oscillatory potential
Rafał Perczyński, Antoni Augustynowicz
Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed t…