A quadratic approximation for solving nonlinear integral equations of Volterra type
Abstract
By using fixed point techniques, we analyze the existence and location of solution of a nonlinear integral equation of Volterra type. These techniques are used to approximate solutions to integral equations of this type, which also allow us to approximate them with quadratic convergence. Besides, we improve this analysis by applying collocation methods based on interpolation polynomials of Lagrange that use zeros of orthogonal Chebyshev polynomials as collocation points. In addition, to solve the sensitivity and ill-conditioning problems that might arise, we apply an Ulm-type iterative method that does not use inverses in the algorithm, but only matrix products.
Fields of Study & Subjects
Iterative Methods for Nonlinear Equations
Mathematical functions and polynomials
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Journal of Computational and Applied Mathematics
- Volume
- 482
- Pages
- 117366–117366
- Publication date
- 14 January 2026
- Language
- EN