Research Information System
New Trends in Mathematical Sciences, vol.6, no.3, pp.24-38, 2018 (Peer-Reviewed Journal)
An advanced matrix method is formulated for the solution of Volterra integro-differential equations with weakly singular kernel by using orthogonal Jacobi polynomials. Employing this practical method, it is possible to solve various types of these equations routinely in a systematic fashion. An error estimation procedure is prescribed to estimate the error of the basic Jacobi method and then the error correction term is added to the basic method to obtain more accurate results. Four test experiments are provided to confirm the validity and systematic approach of the advanced method.These experiments also certified that this advanced method surpasses the basic Jacobi method, as well as several alternative approaches.