Construction of interpolation method for numerical solution of the Cauchy’s problem - Bihun, Roman; Tsehelyk, Gregoriy (Eastern-European Journal of Enterprise Technologies, 2017)
An interpolation numerical method is developed in order to solve the Cauchy’s problem for ordinary first order differential equations using the apparatus of non-classical minorants and diagrams of Newton’s functions, assigned in a tabular form. We have proven computational stability of the method, that is, an error of the initial data is not piled up. It is also shown that the method possesses a second order of accuracy and in the case of a convex function produces more accurate results than the Euler’s method. The advantages also include simplicity and visual clarity of the method. Given this, it could gain widespread use in many areas, in particular mathematics, physics and mechanics. We also give an example of solving the Cauchy’s problem applying the new method, the Euler’s method, and the Runge-Kutta fourth order method, with the results compared. The proposed method does not require solving the systems of linear algebraic equations because we do not employ the Bernstein polynomials, and it is not required to superimpose additional conditions, in contrast to the method that applies the Haar functions