On One Application of Hybrid Methods For Solving Volterra Integral Equations
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51353", author = "G.Mehdiyeva and V.Ibrahimov and M.Imanova", title = "On One Application of Hybrid Methods For Solving Volterra Integral Equations", 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", volume = "6", number = "1", pages = "6-5", }