Open AccessBarycentric Lagrange interpolation for solving Volterra integral equations of the second kind
Author(s) -
E. S. Shoukralla,
H. A. El-Gohary,
B. M. Ahmed
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1447/1/012002
Subject(s) - barycentric coordinate system , mathematics , volterra integral equation , interpolation (computer graphics) , algebraic equation , lagrange polynomial , mathematical analysis , convergence (economics) , collocation method , integral equation , nonlinear system , polynomial , computer science , differential equation , geometry , animation , ordinary differential equation , physics , computer graphics (images) , quantum mechanics , economic growth , economics
An improved version of Barycentric Lagrange interpolation with uniformly spaced interpolation nodes is established and applied to solve Volterra integral equations of the second kind. The given data function and the unknown functions are transformed into two separate interpolants of the same degree, while the kernel is interpolated twice. The presented technique provides the possibility to reduce the solution of the Volterra equation into an equivalent algebraic linear system in matrix form without any need to apply collocation points. Convergence in the mean of the solution is proved and the error norm estimation is found to be equal to zero. Moreover, the improved Barycentric numerical solutions converge to the exact ones, which ensures the accuracy, efficiency, and authenticity of the presented method.