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Dr. Mehriban Imanova

Department of Computational Mathematics, Baku State University, Azerbaijan


Talk Title
On the Comparison of the Gauss method and the Hybrid Methods and their Application to Calculation of Definite Integrals

Talk Abstract


As is known there is the wide class of methods for calculation of the definite integral constructed by the well-known scientists as Newton, Gauss, Chebyshev, Cotes, Simpson, Krylov and etc. It seems that to receive a new result in this area is impossible.

The aim of this work is the applied some general form of hybrid methods to the calculation of definite integral and compares that with the Gauss method. And also are constructed methods, which have applied to calculation of the definite integral with the symmetric bounders. As is known, one of the popular methods for calculation of the definite integrals with the symmetric bounders is the Chebyshev method. Therefore, here have defined some relations between of the above mentioned methods. For the application constructed, here methods are defined the necessary conditions for its convergence. The receive results have illustrated by some model integral.

Short Biography

The scientific field of activity of M.N.Imanova – study of the numerical solution of the initial-value problem for the ODE, investigation of the integro-differential equations of Volterra type. For solving these equations, she has constructed the stable methods with higher order of accuracy and has found for them the region of stability. For this aim, M.N.Imanova applied the multistep methods with the constant coefficients to solving integro-differential equations. M.N.Imanova has constructed some numerical methods of varying quality and has shown them advantages. For the solving practical problems, which can be investigated and described by differential or integro-differential equations, M.N.İmanova proposed to investigation the approximate solution of ordinary differential, integral and integro-differential equations of Volterra type (iteration and numerical methods). Some of  modifications of the quadrature method are used for finding the numerical solution of the integral equations of Volterra type. The basic deficiency of these methods is that the calculation of the values of the solution for the equation at any point reduces to calculation of integral sum with the variable boundary. In other words, the volume of the calculations which are required for finding the values of the solution of the considering equation in general is unbounded. In order to overcome this difficulty, the supervisor of the project must construct the new methods. For application these methods to solving some problems, can be use the predictor-corrector method. The supervisor of the project must construct an effective method for finding numerical solutions of the initial-value problem for arbitrary order ordinary differential equations and must show theirs advantages. She must investigate of the application of the multistep methods to solving integro-differential equations of Volterra type. M.N.İmanova has published the received results in the journals with the higher priority. Imanova has performed about her results at many international conferences (Conference in Numerical Analysis, Book of Abstracts, Chania, Crete, Greece; World Academy of Science, engineering and Technology, Paris, Fransa; International conference on differential equations, difference equations and special functions, Patras, Greece; 9th International conference on mathematical problems in engineering, aerospace and sciences, AIP, Vienna, Austria; World Academy of Science, engineering and Technology, Dubai), Cambridje UK,  and published in the form of papers in many leading journals.

Talk Keywords
The initial-value problem for ODE, definite integral, Gauss method, multistep hybrid method.
Target Audience
Students, Post doctoral, Industry, Doctors and professors
Speaker-intro video

The International Conference on Innovative Applied Energy (IAPE’18)