Abstract
In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate.
Highlights
Integral equations describe many different events in science and engineering fields
The aim of this paper is to present a numerical method by using tight framelets for approximating the solution of a linear Fredholm integral equation of the second kind given by b u(x) = f (x) + λ ∫
To formulate the matrix form and the numerical solution of a given Fredholm integral equation, we will study and use tight framelets and their constructions that are derived from the unitary extension principle (UEP) and the oblique extension principle (OEP) [18]
Summary
Integral equations describe many different events in science and engineering fields. They are used as mathematical models for many physical situations. The study of integral equations and methods for solving them are very useful in application. The aim of this paper is to present a numerical method by using tight framelets for approximating the solution of a linear Fredholm integral equation of the second kind given by b u(x) = f (x) + λ ∫. Many numerical methods use wavelet expansions to solve integral equations, other types of methods work better with redundant systems, of which framelets are the easiest to use. Since 1991, wavelets have been applied in a wide range of applications and methods for solving integral equations.
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