On Some Ways for Application of Hybrid Methods to Solve Odes of the First Order

Abstract

With the investigation of the numerical solution of the ODEs, scientists began studying from  Newton. Consequently, there were constructed many methods for solving the above –mentioned problem. Have suggested conceptions for the comparison of these methods. And in the results of which are constructed class numerical methods for solving initial-value problems for the ODEs. Among of them, the hybrid methods are better, by taking into receiveaccount that these methods are more exact than the others. It is noted that these methods have some disadvantages, which relate with the calculation of the values at the hybrid points of the sought solution of the problems to be solved. Here, have given some ways for solving these problems. The receiving results are compared with the known by using some simple examples.