Abstract
The main aim of this paper is to apply the Hermite trigonometric scaling function on [0, 2π] which is constructed for Hermite interpolation for the linear Fredholm integro-differential equation of second order. This equation is usually difficult to solve analytically. Our approach consists of reducing the problem to a set of algebraic linear equations by expanding the approximate solution. Some numerical example is included to demonstrate the validity and applicability of the presented technique, the method produces very accurate results, and a comparison is made with exiting results. An estimation of error bound for this method is presented.
Highlights
IntroductionIn this paper we solve the Fredholm Linear Integro-Differential Equations as μ0 ( x) + μ1 ( x)u′( x) + μ2 ( x)u′′( x=) g ( x ) + ∫0k x, t u
In this paper we solve the Fredholm Linear Integro-Differential Equations as μ0 ( x) + μ1 ( x)u′( x) + μ2 ( x)u′′( x=) g ( x ) + ∫0k x, t ut dt 0 ≤ x ≤ 1, u (0=) u0, u (1=) u1 (1)where μi ( x), f ( x), and Kl ( x,t ) are given functions that have suitable derivatives, and u0 and u1 are given real constans
Our results indicate that the method with the trigonometric scaling bases can be regarded as a structurally simple algorithm that is conventionally applicable to the numerical solution of IDEs
Summary
In this paper we solve the Fredholm Linear Integro-Differential Equations as μ0 ( x) + μ1 ( x)u′( x) + μ2 ( x)u′′( x=) g ( x ) + ∫0k x, t u. Where μi ( x) , f ( x) , and Kl ( x,t ) are given functions that have suitable derivatives, and u0 and u1 are given real constans. It is difficult to obtain exact solution of the above integration. Various approximation method have been proposed and studied. The purpose of the present paper is to develop a trigonometric Hermite wavelet approximation for the computing of the problem [1]
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