**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**33030

##### Research of a Multistep Method Applied to Numerical Solution of Volterra Integro-Differential Equation

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

**Abstract:**

**Keywords:**
Volterra integro-differential equations,
multistepmethods,
finite-difference methods,
initial value problem

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1076702

**References:**

[1] V.Volterra, "Theorie of functionals and of integral and integrodifferential equations" London, 1931.

[2] Ye. M. Polishuk, Vito Volterra. Leningrad, nauka, 1977, 114 p.

[3] M.N. Imanova, "Numerical solution of Volterra integro-differential equation" Proceeding of institute of mathematics and mechanics, XXII, Baku, 2005.

[4] H.Brunner,"Implicit Runqe-Kutta methods of optimal order for Volterra inteqro-differential equations" Vol 442, Ôäû106, January 1984, pp.95- 109.

[5] Ch.Lubich, "Runge-Kutta theory for Volterra and Abel integral equations of the second kind" Mathematics of computation volume 41, number 163, July 1983, p. 87-102.

[6] V.R. Ibrahimov, "On the maximum degree of the k-step Obrechkoff-s method" Bulletin of Iranian Mathematical Society, Vol. 20, No. 1, pp.1-28 (2002).

[7] V.R. Ibrahimov, M.N. Imanova, "On the new method for solving Volterra integral equation" Transactions issue mathematics and mechanics series of physical-technical and mathematical science, XXVI, Ôäû1, 2007.

[8] V.R. Ibrahimov, G.Yu.Mehdiyeva, "On way of generalizing quadrature method", Baku State University, series of physicomath. sciences, 1, 2008, p.92-88.

[9] A.F. Verlan, V.S. Sizikov, "Integral equations: methods, algorithms, programs" (In Russian) Naukova Dumka, Kiev (1986), 544 p.

[10] G. Dahlquist, "Convergence and stability in the numerical integration of ordinary differential equations" Math. Scand. - 1956, Ôäû4, p.33-53.