COLLOCATION METHOD FOR SOLVING HIGH ORDER VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

COLLOCATION METHOD FOR SOLVING HIGH ORDER

Abstract

This paper presents a method of solving high order Volterra integro-differential equations (VIDEs) of second, third, and fourth orders using polynomial collocation methods. The accuracy and efficiency of polynomial approximations ranging from cubic to decic degrees, employing Chebyshev-Gauss-Lobatto collocation points were systematically investigated. The method was subsequently applied to several benchmark problems, and results validated against known analytical solutions. The results demonstrate that: second-order VIDEs require sextic polynomials for machine precision, third-order VIDEs require septic polynomials and fourth-order VIDEs require nonic polynomials.