Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions

Abstract

In this article, we consider a class of nonlinear functional integral equations which has rather general form and contains a lot of particular cases such as functional equations and nonlinear integral equations of Volterra type. We use a combination of a fixed point method and cubic semiorthogonal B‐spline scaling functions to solve the integral equation numerically. We provide an error analysis for the method which shows that the approximate solution converges to the exact solution. Some numerical results for several test problems are given to confirm the accuracy and the ease of implementation of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 699–722, 2014

Iterative solution of a class of nonlinear Fredholm integral equations

“…Few authors have considered the numerical approximation of functional integral equations [1,9], motivating the present work to use the strategy known as fixed-point (Picard) iteration [2], together with the collocation discretization, to find an approximate solution u (k) to a solution of eq. (3).…”

Reliability and Availability Analysis of Process Systems under Changing Operating Conditions

“…Volterra integral equations are also used in stochastic models that can deal with not only changing operating conditions but also process uncertainties as proposed by Deng et al (2013). Numerical solution techniques for Volterra integral equations are also being developed as studied by Maleknejad et al (2014). …”

Numerical Solution of Fractional Volterra-Fredholm Integro-Differential Equation Using Lagrange Polynomials

“…Mohammed (2) in 2014 investigated numerical solution of LFIDE's by the least squares method with the aid of shifted Chebyshev polynomial. Maleknejad et al (4) in 2013 presented a numerical scheme, based on the cubic B-spline wavelets for solving fractional integrodifferential equations. Mohamed et al (5) in 2016 introduced an analytical method, called homotopy analysis transform method (HATM) which is a combination of HAM and Laplace decomposition method, this scheme is applied to linear and nonlinear fractional integro-differential equations.…”

“…While section (3) presents the derivation of the proposed methods. Section (4) proposes the general algorithm for the method. Test examples are given in section (5) including general and special cases of LFVFIDE to improve the capability of the proposed method to solve various type of equation in addition with LFVFIDE, in all the test examples ( ) is chosen in such a way that we know the exact solution.…”