Numerical solutions of the nonlinear fuzzy Hammerstein–Volterra delay integral equations

New error estimation based on midpoint iterative method for solving nonlinear fuzzy fredholm integral equations

“…Theorem 4. Assume (7) satisfies the conditions of lemma (4), then the iterative procedure (7), converges to the unique solution of E.q. (1), u * , and its error estimate is as follows…”

“…In order to investigate the numerical stability of (7) with respect to small perturbation in the starting approximation, we consider another starting approximation v 0 ∈ C [a, b] such that there exists ε > 0 for which D(u 0 (x), v 0 (x)) < ε, ∀x ∈ [a, b]. The following sequence of successive approximations is obtained as follows:…”

Numerical solution of two dimensional nonlinear fuzzy Fredholm integral equations of second kind using hybrid of block-pulse functions and Bernstein polynomials

“…Numerical procedures for solving fuzzy integral equations of the second kind, based on the successive approximation method and other iterative techniques, have been investigated in [6,24]. Recently, Bica and Popescu [7,8] applied the successive approximation method to the fuzzy Hammerstein integral equation. Ezzati and Ziari [9] proved the convergence of the successive approximation method for solving nonlinear fuzzy Fredholm integral equations of the second kind, and they proposed an iterative procedure based on the trapezoidal quadrature.…”

Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method

“…During the last decades, many authors have devoted their attention to study solutions to uncertain integral equations using various numerical and analytical methods. Among these attempts are the homotopy analysis method [11], Adomian decomposition method [12], homotopy perturbation method [13], Lagrange interpolation method [14], differential transform method [15], and other methods [16][17][18]. The purpose of this paper is to extend the application of the reproducing kernel Hilbert space (RKHS) method to provide 2 Journal of Function Spaces analytic-numeric solutions for a class of uncertain Volterra integral equations of the second kind in the following form:…”