О решении задачи коши с помощью решетчатых функций в математической физике и химической кинетике

A polynomial method of Cauchy problem solving is presented. The method allows constructing a fundamental solution in locally analytical form for any type of function of the right part of the equation for normal form of differential equation. A test for well-known functions both for lower and higher among possible orders of polynomial method of solving is carried out. The expediency of using the method of higher order is determined.