Canonical basis interpolation method of solving initial-value problems

Abstract

This paper is focused on the numerical solution of initial-value problems of ordinary differential equations, using Newton's interpolation method and Lagrange method. New canonical polynomials are constructed and used as basis functions. The Lanczos method is adopted for the construction of the polynomials to certain degrees, whereby a recursive relation is developed to generate a set of canonical polynomials. Hence, these Canonical polynomials in combination with the Newton interpolation and Lagrange method are utilized for the approximation of the unknown functions and differential functions in the given differential equations. The effectiveness and efciency of the method is evidently ascertained as it is applied on some test problems.