## Abstract

Integral equations of Volterra type arise quite naturally in physical applications modelled by initial-value problems. Consider the linear Volterra equation of the second kind. (Fredholm equations of the second kind which are associated with boundary value problems for a fmite interval [a,b], are similar except that the upper limit is b.)

with a ≤ x, y ≤ b, and let

*λ*= 1. Using decomposition , we identify*φ*_{0}= f(x) assuming f(x) ≠ 0, then and write as the solution, or with an m-term approximant . In some cases, exact solutions are determinable. Consider an example:

Then

Thus the two-term approximant is

or

*φ*= sin x as is easily verified either by calculating more terms or by substitution.## Preview

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## Reference

- 1.Y. Cherruault, G. Saccomandi, and B. Some, New Results for the Convergence of Adomian’s Method Applied to Integral Equations,
*Math. Comput. Modelling*,**16**, (8593) (1992).Google Scholar

## Suggested Reading

- 1.G. Adomian,
*Nonlinear Stochastic Operator Equations*, Academic Press, New York (1986).Google Scholar - 2.B. Some, Some Recent Numerical Methods for Solving Hammersteins Integral Equations,
*Math. Comput. Modelling*, to appear.Google Scholar - 3.B. Some, A New Computational Method for Solving Integral Equations, submitted for publication.Google Scholar

## Copyright information

© Springer Science+Business Media Dordrecht 1994