Open AccessOn the numerical solutions for nonlinear Volterra-Fredholm integral equations
Author(s) -
Parviz Darania,
S. Pishbin
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.42815
Subject(s) - mathematics , nonlinear system , convergence (economics) , coefficient matrix , integral equation , diagonal , collocation method , stability (learning theory) , fredholm integral equation , volterra integral equation , mathematical analysis , computation , collocation (remote sensing) , numerical analysis , fredholm theory , matrix (chemical analysis) , computer science , eigenvalues and eigenvectors , differential equation , physics , geometry , algorithm , ordinary differential equation , materials science , quantum mechanics , composite material , machine learning , economics , economic growth
In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an efficient implementation. Convergence analysis and linear stability estimates are investigated. Finally numerical experiments are given, which confirm our theoretical results.