{"title":"On a Way for Constructing Numerical Methods on the Joint of Multistep and Hybrid Methods","authors":"G.Mehdiyeva, M.Imanova, V.Ibrahimov","country":null,"institution":"","volume":57,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1488,"pagesEnd":1492,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/15043","abstract":"Taking into account that many problems of natural\r\nsciences and engineering are reduced to solving initial-value problem\r\nfor ordinary differential equations, beginning from Newton, the\r\nscientists investigate approximate solution of ordinary differential\r\nequations. There are papers of different authors devoted to the\r\nsolution of initial value problem for ODE. The Euler-s known\r\nmethod that was developed under the guidance of the famous\r\nscientists Adams, Runge and Kutta is the most popular one among\r\nthese methods.\r\nRecently the scientists began to construct the methods preserving\r\nsome properties of Adams and Runge-Kutta methods and called them\r\nhybrid methods. The constructions of such methods are investigated\r\nfrom the middle of the XX century. Here we investigate one\r\ngeneralization of multistep and hybrid methods and on their base we\r\nconstruct specific methods of accuracy order p = 5 and p = 6 for\r\nk = 1 ( k is the order of the difference method).","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 57, 2011"}