Geodesic
Theoretical investigation on error analysis of Sinc approximation for mixed Volterra–Fredholm integral equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5 
H. Mesgarani; R. Mollapourasl. Theoretical investigation on error analysis of Sinc approximation for mixed Volterra–Fredholm integral equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a1/
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     author = {H. Mesgarani and R. Mollapourasl},
     title = {Theoretical investigation on error analysis of {Sinc} approximation for mixed {Volterra{\textendash}Fredholm} integral equation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this study, we propose one of the new techniques used in solving numerical problems involving integral equations known as the Sinc-collocation method. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this article, a mixed Volterra–Fredholm integral equation which has been appeared in many science an engineering phenomena is discredited by using some properties of the Sinc-collocation method and Sinc quadrature rule to reduce integral equation to some algebraic equations. Then exponential convergence rate of this numerical technique is discussed by preparing a theorem. Finally, some numerical examples are included to demonstrate the validity and applicability of the convergence theorem and numerical scheme.

[1] S. Gorenflo, S. Vessella, Abel integral equations. Analysis and applications, Springer, Berlin, 1991 | MR

[2] E. G. Ladopoulos, Singular Integral Equations: Linear and Nonlinear Theory and Its Applications in Science and Engineering, Springer, Berlin, 2000 | MR | Zbl

[3] K. Maleknejad, E. Najafi, “Numerical solution of nonlinear Volterra integral equations with nonincreasing kernel and an application”, Bull. Malays. Math. Sci. Soc., 34:2 (2011), 379–388 | MR | Zbl

[4] R. P. Agarwal, J. Banas, R. Mollapourasl, T. Gnana Bhaskar, “On solutions of a generalized neutral logistic differential equation”, Adv. Stud. Contemp. Math. (Kyungshang), 20:2 (2010), 279–290 | MR | Zbl

[5] P. Maleknejad, R. Torabi, R. Mollapourasl, “Fixed point method for solving nonlinear quadratic Volterra integral equations”, Comput. Math. Appl., 62 (2011), 2555–2566 | DOI | MR | Zbl

[6] A. N. Sidorov, M. V. Falaleev, D. N. Sidorov, “Generalized solutions of Volterra integral equations of the first kind”, Bull. Malays. Math. Sci. Soc. (2), 29:1 (2006), 101–109 | MR | Zbl

[7] B. Rzepecki, “Measure of noncompactness and Krasnosel'skii's fixed point theorem”, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 24 (1976), 861–865 | MR

[8] W. Volk, “The iterated Galerkin methods for linear integro-differential equations”, J. Comp. Appl. Math., 21 (1988), 63–74 | DOI | MR | Zbl

[9] F. Maleknejad, F. Mirzaee, “Using rationalized Haar wavelet for solving linear integral equations”, Appl. Math. Comp., 160 (2005), 579–587 | DOI | MR | Zbl

[10] A. Avudainayagam, G. Vani, “Wavelet Galerkin method for integro-differential equations”, Appl. Numer. Math., 32 (2000), 247–254 | DOI | MR | Zbl

[11] F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer-Verlag, New York, 1993 | MR | Zbl

[12] X. Shang, D. Han, “Numerical solution of Fredholm integral equations of the first kind by using linear Legendre multiwavelets”, Appl. Math. Comput., 191 (2007), 440–444 | DOI | MR | Zbl

[13] E. Babolian, Z. Masouri, “Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions”, J. Comput. Appl. Math., 220 (2008), 51–57 | DOI | MR | Zbl

[14] E. Babolian, T. Lotfi, M. Paripour, “Wavelet moment method for solving Fredholm integral equations of the first kind”, Appl. Math. Comput., 186 (2007), 1467–1471 | DOI | MR | Zbl

[15] B. Bialecki, “Sinc-collocation methods for two-point boundary value problems”, IMA J. Numer. Anal., 11 (1991), 357–375 | DOI | MR | Zbl

[16] J. Lund, “Symmetrization of the Sinc-Galerkin method for boundary value problems”, Math. Comput., 47 (1986), 571–588 | DOI | MR | Zbl

[17] J. Lund, K. L. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Philadelphia, 1992 | MR | Zbl