**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30750

##### On a Way for Constructing Numerical Methods on the Joint of Multistep and Hybrid Methods

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

**Abstract:**

**Keywords:**
initial value problem,
Multistep and hybrid methods,
degree and stability of hybrid methods

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1084278

**References:**

[1] Subbotin M.F. Course of selestial mechanics. Vol.2, M, ONTI, 1937, 404 p. (Russian).

[2] C.S Gear. Hybrid methods for initial value problems in ordinary differential equations. SIAM, J. Numer. Anal. v. 2, 1965, pp. 69-86.

[3] 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.

[4] 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.

[5] V.R. Ibrahimov. On a nonlinear method for numerical calculation of the Cauchy problem for ordinary differential equation, Diff. equation and applications. Pros. of II International Conference Russe. Bulgarian, 1982, pp. 310-319.

[6] A. Makroglou. Hybrid methods in the numerical solution of Volterra integro-differential equations. Journal of Numerical Analysis 2, 1982, pp.21-35.

[7] G.Mehdiyeva, M.Imanova, V.Ibrahimov Application of the hybrid methods to solving Volterra integro-differential equations World Academy of Science, engineering and Technology, Paris, 2011, 1197- 1201.

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