# Vagif Rza Ibrahimov

Vagif Rza Ibrahimov (born May 9, 1947, in the village of Jahri) is an Azerbaijani mathematician and professor. He is a corresponding member of ANAS and an organizer and a participant of numerous conferences. He has published more than 102 articles abroad. He is a professor at Baku State University.

## Biography

Vagif Rza Ibrahimov is a corresponding member of ANAS, doctor of Physical and Mathematical Sciences, membership of American Mathematical Society and European Mathematical Society, organizer and participant of numerous conferences, keynote speaker of the international conference IAPE'19 Oxford, Honored Teacher of the Republic of Azerbaijan and winner of 1st World Science Championship in Dubai.
Doctor of Physical and Mathematical Sciences, V.R. Ibrahimov, for investigation of the forward jumping methods, extrapolation and interpolation methods in the general form, has constructed several formulas by which one can determine the upper bound for the accuracy to explicit and implicit stable multistep methods Obreshkov type, such he expanded Dalqvist's theory. For the first time, he proved the advantages of the forward jumping methods, and he constructed special methods such as predictor-correction for their use. He proved that there are more precise forward jumping methods. V.R. Ibrahimov found the maximum values of the degrees of stable and unstable MMM (including Cowell type methods) thus the study of the relationship between order and degree for MMM can be considered complete. V. Ibrahimov received a special representation of the error of the multi-step method, with which he determined the maximum number of increase in the accuracy of the method after a single application of Richardson extrapolation and a linear combination of multi-step methods. To construct more precise methods, he proposed using hybrid methods, which he applied to the solving first-order and second-order ordinary differential equations. V.R. Ibrahimov defined the relations between of some coefficients for the MMM (including methods with forward jumping), which are the main criterion in the construction of stable multistep methods Obreshkov type with the maximal degree. These relations can be applied to the construction of two-sided methods. It is these methods that allow us to find the interval in which the exact value of the solution of the original problem lies.
V.R. Ibrahimov constructed special methods for solving integral equations of Volterra type, in which the number of calculations of the integral kernel at each step remains constant. He defined sufficient conditions for their convergence. Taking into account that these methods represent new directions in the theory of numerical methods for solving integral equations, he constructed methods at the junction of multi-step and hybrid methods applied to the solving of integral and integro-differential equations of Volterra type. V.R. Ibrahimov constructed methods with an extended stability region for solving integral and integro-differential equations of Volterra type using special test equations. To solve integral equations of Volterra type with symmetric boundaries, he proposed using symmetric methods and constructed special symmetric methods of the forward jumping type. In order to construct stable methods having higher accuracy and an extended stability region, V.R. Ibrahimov proposed to construct methods at the junction of hybrid and forward jumping methods, which applied to the solving of the ODE, integral and integro-differential equations of Volterra type.

## Honours and awards

2023 - Winner of the World Science Championship held in Dubai (1st place).
2019-2023 - Grant provided by the Science Development Fund under the President of the Republic of Azerbaijan.
2019 - Order of Glory
2014- Diploma awarded by the Foundation for the Development of Science under the President of the Republic of Azerbaijan, the Ministry of Communications and High Technologies of the Republic of Azerbaijan and the State Commission of the Republic of Azerbaijan by UNESCO (awarded second place for the best work in the field of ICT).
2011-2014 -Grant issued by the Foundation for the Development of Science under the President of the Republic of Azerbaijan.
2016-2019 -Grant issued by the Foundation for the Development of Science under the President of the Republic of Azerbaijan.
2011 - Diploma "Development of Science", issued by the international organization ASHE London.
2009 - Honored Teacher of the Azerbaijan Republic [1].

## Career

From 2022 to the present - Head, Department of Computational Mathematics [2], BSU.
From 2005 to the present time, Professor of the Department of Computational Mathematics [2], BSU.
2004-2011 - Vice-Rector, BSU.
2000-2004 - Head of the Department of Computational Mathematics [2], BSU.
1985-2005 - Associate Professor, Department of Computational Mathematics [2], BSU.
1982-1985 - Senior Lecturer, Department of Computational Mathematics [2], BSU.
1975-1982 - Assistant, Chair of Computational Mathematics [2], BSU.
1972-1975 - Post-graduate student, Faculty of Mechanics and Mathematics, BSU.
1970-1972 -Service in the ranks of the Soviet Army.
1969-1970 - laboratory assistant, Department of Computational Mathematics [2], BSU.

## Publications

* Multistep methods for solving the Cauchy problem for ordinary differential equations: Thesis for the soc. scientist. step. Doctor of Phys.-Math. Sciences: 01.01.07
* Some properties of Richardson extrapolation. Diff. Eq. No. 12,1990.
* A relationship between order and degree for a stable formula with advanced. J. Comput. mat. and mat.phys., No. 7 ,1990.
* On the maximal degree of the k-step Obrechkoffs method. Bulletin of Iranian Mathematical Society.Vol.28, №1,2002.
* On one application of forward jumping methods. Applied Numerical Mathematics . Volume 72, October 2013
* Application of the hybrid method with constant coefficients to solving the integro-differential equations of first order. World Congress: 9th International conference on mathematical problems in engineering, aerospace and sciences, Vienna, Austria, 10-14 July 2012.
* The application of the hybrid method to solving the Volterra integro-differential equation. World Congress on Engineering 2013, London, U.K., 3-5 July, 2013.
* On the research of multistep methods with constant coefficients. Monograph LAP LAMBERT Academic Publishing, 2013.
* On a Research of Hybrid Methods, Numerical Analysis and Its Applications, Springer, 2013,p. 395-402.
* A way to construct an algorithm that uses hybrid methods, Applied Mathematical Sciences, HIKARI Ltd, Vol. 7, 2013, no. 98. ,p.4875-4890.
* The construction of the finite-difference method and application, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014) AIP Conf. Proc. 1648, © 2015 AIP Publishing LLC,850049-1–850049-5.
* The application of second derivative methods to solving Volterra integro-differential equations, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014) AIP Conf. Proc. 1648, © 2015 AIP Publishing LLC ,850048-1–850048-4.
* On the application of multistep methods to solving some problems of communication, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014) AIP Conf. Proc. 1648, © 2015 AIP Publishing LLC, 850050-1–850050-5.
* Solving Volterra Integro-Differential Equation by the Second Derivative Methods, Applied Mathematics and Information Sciences, Volume 9, No. 5, Sep. 2015, pp. 2521-2527.
* General Theory of the Application of Multistep Methods to Calculation of the Energy of Signals ,Wireless Com100munications, Networking and Applications Volume 348 of the series Lecture Notes in Electrical Engineering, Springer 1047-1056.
* Some refinement of the notion of symmetry for the Volterra integral equations and the construction of symmetrical methods to solve them,Journal of Computational and Applied Mathematics, 306 (2016), 1–9.
* John Butcher and hybrid methods, AIP Conference Proceedings 1863, 560029(2017); doi: http://aip.scitation.org/doi/abs/10.1063/1.4992712