Solutions of Fredholm integral equations via discrete biquintic splines

Abstract

a b s t r a c tTo find approximate solutions of Fredholm integral equations, we degenerate the kernels by discrete biquintic splines. Explicit a priori and a posteriori error bounds are derived and a numerical example is presented to confirm the theoretical results.

Convergence analysis and parity conservation of a new form of a quadratic explicit spline with applications to integral equations

“…An interesting work is [5] where Chebyshev's polynomials are used. Finally, in [7], splines of order five are used. Here, the quadratic spline determined by our method is applied to numerically solve the linear problem.…”

“…There are many works which have analyzed and proposed numerical methods, as well as other based on the methods of splines. A recent interesting work is [5] in which they apply the collocation method using Chebyshev's polynomials to numerically evaluate the problem of Fredholm-Volterra; in [6] this kind of integral, equations are solved with B-Splines; in [7], fifth-order splines are used; in [8], the quadratic spline with end condition is utilized; and in [9], variable-order fractional functional differential equations are solved with Legendre collocation. In the present article, the spline obtained is used to solve Fredholm-Volterra integral equations and fractional differential equations.…”

Convergence analysis and parity conservation of a new form of a quadratic explicit spline

“…There exist numerous works to determine the numerical solution of Fredholm linear integral equations of the first and second kind [6,7,8,9,10]. Following, the results of the previous sections are applied to numerically solve the linear problem.…”

Performance analysis of Half-Sweep AOR iterative method in solving second kind Linear Fredholm Integral Equations

“…In this paper, numerical solutions for linear Fredholm integral equations of the second kind, given by ( ) ( )( ) ( ) In recent years, some efficient numerical methods for solving problem (1) have been proposed, for instance, some very recent references are [1][2][3][4][5]. The fundamental concept of the numerical methods is to reduce the problem in the form of a finite-dimensional linear system which is mostly dense.…”