10.1186/2251-7456-6-60

An iterative scheme for numerical solution of Volterra integral equations using collocation method and Chebyshev polynomials

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  • Jalil Rashidinia1,
  • Esmaeil Najafi*2,
  • Asghar Arzhang3,
  1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846 13114, IR
  2. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846 13114, IR Department of Mathematics, Urmia University, Urmia, IR
  3. Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IR
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Published in Issue 2012-10-30

How to Cite

Rashidinia, J., Najafi, E., & Arzhang, A. (2012). An iterative scheme for numerical solution of Volterra integral equations using collocation method and Chebyshev polynomials. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-60
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Abstract

Abstract Abstract When we discretize nonlinear Volterra integral equations using some numerical, such as collocation methods, the arising algebraic systems are nonlinear. Applying quasilinear technique to the nonlinear Volterra integral equations gives raise to linear Volterra integral equations. The solutions of these equations yield a functional sequence quadratically convergent to the solution. Then, we use collocation method based on Chebyshev polynomials and a modified Clenshaw-Curtis quadrature and obtain a numerical solution. Error analysis has been performed, and the method has been applied on three numerical examples.

Keywords

  • Volterra integral equations,
  • Quasilinear technique,
  • Collocation method,
  • Chebyshev polynomials
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