An Application of Mathematical Methods for Solving of Scientific Problems

As is known, the formation and development of the mathematical methods are largely related with the successful application of these methods to solve problems of the natural sciences. Recently the area of application of the mathematical methods is greatly expanded. It is difficult to find an area where it is not used in solving different problems. As is known, is appeared the necessity to solve the differential, integral and integro-differential equations in solving of scientific problems. Note that one of the basic questions in the modern computational mathematics consists of construction of the numerical methods with the high accuracy. Therefore, here, is proposed the multi-step method with higher accuracy than the known. And is constructed the stable methods with the expanded area of stability for solving the above mentioned equations.