Numerical iterative method for Volterra equations of the convolution type

Abstract

The objective of this paper is to present an algorithm from which a rapidly convergent solution is obtained for Volterra integral equations of Hammerstein type. Such equations are often encountered when describing the response of viscoelastic materials where the time dependency of the material properties is often expressed in the form of a convolution integral. Frequently, singularity is encountered and often ignored when dealing with the constitutive equations of viscoelastic materials. In this paper, the singularity is incorporated in the solution and the iterative scheme used to solve the equation converges within six iterations to a typical toleration error of 10−5. The algorithm is applied to the strain response of a polymer under impulsive (constant) loading and the results show excellent correlation between the experimental and analytical solution. Copyright © 2010 John Wiley & Sons, Ltd.