Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
Application of the Hybrid Methods to Solving Volterra Integro-Differential Equations

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

Abstract:

Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra integro-differential equations. The way for defining the coefficients of the suggested method is also given.

Keywords: Integro-differential equations, initial value problem, hybrid methods, predictor-corrector method

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076842

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1308

References:


[1] V.Volterra. Theory of functional and of integral and integrodifferential equations. Moscow, Nauka, 1982, 306 p.
[2] M. James, G. Ortega William, Jr. Poole. An introduction to numerical methods for differential equations. Moscow, Nauka, 1986, 288 p.
[3] A. Makroglou. Hybrid methods in the numerical solution of Volterra integro-differential equations. Journal of Numerical Analysis 2, 1982, pp.21-35
[4] Sovremenniye chislenniye metodi obiknovennix differensialnix uravneniy. (J.Holl, J.Uatt), 1979,312 p.
[5] Butcher J.C. A modified multistep method for the numerical integration of ordinary differential equations. J. Assoc. Comput. Math., v.12, 1965, pp.124-135.
[6] G.K. Gupta. A polynomial representation of hybrid methods for solving ordinary differential equations, Mathematics of comp., volume 33, number 148, 1979, pp.1251-1256
[7] C.S Gear. Hybrid methods for initial value problems in ordinary differential equations. SIAM, J. Numer. Anal. v. 2, 1965, pp. 69-86.
[8] R.R. Mirzoyev, G.Yu Mehdiyeva., V.R. Ibrahimov, On an application of a multistep method for solving Volterra integral equations of the second kind, Proceeding the 2010 International Conference on Theoretical and Mathematical Foundations of Computer Science, Orlando, USA, 2010, pp. 46-50.
[9] G.Dahlquist Convergence and stability in the numerical integration of ordinary differential equations. Math. Scand. 1956, Ôäû4, p.33-53.
[10] 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.
[11] Duglas J.F., Burden R.L. Numerical analysis, 7 edition Cengage Learning 2001,850 pp.
[12] M.N. Imanova, G.Yu. Mehdiyeva, V.R. Ibrahimov. Research of a multistep method applied to numerical solution of Volterra integrodifferential equation, World Academy of Science, Engineering and Technology, Amsrterdam, 2010, pp.349-352