Piecewise interpolation solution of ordinary differential equations with application to numerical modeling problems

Abstract

Piecewise interpolation approximation of functions of one real variable, derivatives and integrals is constructed with the help of Lagrange and Newton interpolation polynomials. The polynomials are transformed to the form of algebraic polynomials with numerical coefficients by means of restoring the polynomial coefficients by its roots. Formulas different from Vieta’s formulas are applied. In the resulting form, the polynomials interpolate the right-hand sides of ordinary differential equations, the expression of the antiderivative ones is used to approximate the solution. Iterative refinement is performed. Error estimates and results of numerical experiments for stiff and non-stiff problems in physical, chemical models and other processes are presented.