An application of Romberg extrapolation on quadrature method for solving linear Volterra integral equations of the second kind Mladen Mes ˇtrovic ´ * , Eva Ocvirk Faculty of Civil Engineering, University of Zagreb, Croatia Abstract The Romberg extrapolation is applied on quadrature method solution of linear Volterra integral equations (VIE) of the second kind. An algorithm for new solution calculated by Romberg method is given. The calculated solutions show more efficiency and accuracy with less computation than solution with quadrature method over more points of integration. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Romberg extrapolation; Quadrature method; Linear Volterra integral equations of the second kind 1. Introduction to linear VIE of the second kind The Volterra integral equation aries in many problems of physics and other areas, in the particle transport problems of astrophysics, potential theory and Dirichlet problem, electrostatics and radiative heat transfer problems. Some different valid methods for solving integral equation have been developed in last years [1–3]. We consider the linear Volterra integral equations of the second kind. The general form of the linear VIE of the second kind is uðxÞ¼ f ðxÞþ Z x a kðx; tÞuðtÞdt; a 6 x 6 b: ð1Þ The functions f(x) and kðx; tÞ, called the kernel of integral equation, are known and u(x) is the unknown func- tion to be determined. 0096-3003/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2007.04.043 * Corresponding author. E-mail addresses: mestar@grad.hr (M. Mes ˇtrovic ´), ocvirk@grad.hr (E. Ocvirk). Available online at www.sciencedirect.com Applied Mathematics and Computation 194 (2007) 389–393 www.elsevier.com/locate/amc