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On One Application of Hybrid Methods For Solving Volterra Integral Equations

Authors: G.Mehdiyeva, V.Ibrahimov, M.Imanova

Abstract:

As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.

Keywords: Volterra integral equation, hybrid methods, stability and degree, methods of quadrature

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1056687

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References:


[1] Polishuk Ye. M. Vito Volterra. Leningrad, Nauka, 1977, 114p.
[2] V.Volterra. Theory of functional and of integral and integro-differensial equations, Dover publications. Ing, New York, 304.
[3] Verlan A.F., Sizikov V.S. Integral equations: methods, algorithms, programs. Kiev, Naukova Dumka, 1986.
[4] Manjirov A.V., Polyanin A.D. Reference book on integral equation. Solution methods. M., Factorial press", 2000, p.384.
[5] Mehdiyeva G.Yu., Imanova M.N., Ibrahimov V.R. A modification of the method of quadratures. Baku State University, series of physicomath. sciences, 2009,Ôäû3, Ðü.101-108
[6] A. Makroglou. Hybrid methods in the numerical solution of Volterra integro-differential equations. Journal of Numerical Analysis 2, 1982, pp.21-35
[7] Mehdiyeva G.Yu., Imanova M.N., Ibrahimov V.R. On one generalization of hybrid methods. Proceedings of the 4th international conference on approximation methods and numerical modeling in environment and natural resources, Saidia, Morocco, may 23-26, 2011, 543-547.
[8] V.R. Ibrahimov. On a nonlinear method for numerical calculation of the Cauchy problem for ordinary differential equation, Diff. equation and applications. Pron. of II International Conference Russe. Bulgarian, 1982, pp. 310-319.