Open AccessSome Advantages of the Hybrid Methods, Which Used the First Derivative of the Solution of the Considered Problem
Author(s) -
Galina Mehdiyeva,
Mehri̇ban İmanova,
Vagif Ibrahimov
Publication year - 2022
Publication title -
international journal of mathematical models and methods in applied sciences
Language(s) - English
Resource type - Journals
ISSN - 1998-0140
DOI - 10.46300/9101.2022.16.8
Subject(s) - ode , bernoulli differential equation , derivative (finance) , initial value problem , mathematics , euler's formula , ordinary differential equation , order (exchange) , cauchy distribution , bernoulli's principle , value (mathematics) , type (biology) , differential equation , calculus (dental) , computer science , mathematical analysis , differential algebraic equation , physics , medicine , ecology , statistics , dentistry , finance , biology , financial economics , economics , thermodynamics
The scientists began investigate of the solution of ODE from the XVII century. Many famous mathematicians as Newton, Leibniz, Bernoulli, D’ Alembert, Euler, Cauchy and etc. have considered solving of the ordinary differential equations. For solving these equations the scientists from the different country have constructed many methods. Here, with the help of the compare known results are shown some advantages of the hybrid methods. Are constructed the hybrid methods with the order of accuracy p = 8k . Here, is suggested concrete hybrid method of the fractional step type with the order of accuracy p = 8 for k =1 for which uses the first order derivative of the solution of the initial value problem.