**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31742

##### Application of the Hybrid Methods to Solving Volterra Integro-Differential Equations

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

**Abstract:**

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

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

**References:**

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[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