Notes Acad. USSR 47 , , Kuipers, L. Uniform Distribution of Sequences. New York: Wiley, Postnikov, A.

Steklov Inst. Sloane, N. Stoneham, R.

## Open Mathematics

Wagon, S. Weisstein, E. Wells, D. Middlesex, England: Penguin Books, p. Weisstein, Eric W.

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## Normal distribution - Wikipedia

March , Cite as. This paper presents a numerical method for solving a mixed Fredholm—Volterra linear integral equation of the second kind in a Banach space.

The ideas are interesting and this area caught the attention of many researchers, having so many applications. This paper starts with a brief introduction in the subject and then proposes a new scheme which is discussed in details. The numerical examples in Sect. The authors would like to thank the referees and the editor for the valuable suggestions to improve the writing of this paper. Skip to main content.

Advertisement Hide. A study of normality and continuity for mixed integral equations. Authors Authors and affiliations M.

Abdou M. Nasr M. Article First Online: 27 January Mohamed Abdella.

International Journal of Mathematical Analysis Vol. Abdou, M. Nasr and M. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Also, the normality and the continuity of integral operator are discussed. Finally, numerical results are discussed and the error estimate is computed.

Abdel-Aty 1 Introduction Many problems of mathematical physics, contact problems in the theory of elasticity and mixed problems of mechanics of continuous media are reduced to mixed type of integral equations, see [1,11]. For this many different methods are used to solve the integral equations analytically, see [6—8]. In addition, for numerical methods, we refer to [5]. Phase-Lag has a very important role in our applied life and there are cur- rently One, Dual and Three-Phases and each phase has a different applications.

## Study of the normality and continuity for the mixed integral equations with phase-lag term

For example, the Three-Phase-Lag model incorporates the microstructural in- teraction effect in the fast-transient process of heat transport, see [4]. In this paper, we consider the Fredholm-Volterra integral equations of the second kind with continuous kernels with respect to position and time. We use a numerical method to transform the Fredholm-Volterra integral equations to a linear system of Fredholm integral equations [2, 9]. These equations were named after the leading mathematicians who have first studied them such as Fredholm, Volterra. Fredholm and Volterra equations are the most encountered types.

There is, formally only one differ- ence between them, in the Fredholm equation the region of integration is fixed where in the Volterra equation the region is variable. Integro-Differential Equa- tions IDEs are given as a combination of differential and integral equations. In the recent study there is a growing interest to solve Integro-Differential Equations [10, 12]. Integrating Eq. More information for the characteristic points and the quadrature coefficients are found in [5].