An integro-collocation method for determining initial values for ordinary differential equations

The collocation method used to formulate an integrated Lanczos Tau method for solving ordinary differential equations with starting values is the subject of this research. In order to uniquely determine the coefficients of the approximant of the solution, an algebraic system of linear equations is created by collocating the perturbed integrated equation at certain equally spaced intervals within the range of integration of the differential equation. The method is used to solve problems involving first- and secondorder ordinary differential equations, and data collected from numerical analysis supports its correctness and efficacy.