The Analytical Methods Of Volterra Integral Equations of The Second Kind

Authors

  • Issa H. Al-Aidi University of Wasit. College of Pure Science Education,Wasit,Iraq
  • Ahmed Sh. Al-Atabi Directorate General of Wasit Education, Wasit,Iraq

DOI:

https://doi.org/10.31185/wjcms.119

Keywords:

Domain Decomposition, Successive Approximation Technique, Laplace Transformation, Modified Decomposition

Abstract

This paper discussed the analytic methods to solve Second order Volterra integral equations form using different methods. The domain decomposition method is the first technique. Depending on the hypothesis, the solution is by sequence. The second method is the successive approximation technique, which is used Picard iteration method. The third method used Laplace transformation. The modified decomposition technique is used as the fourth method. Depending on the Taylor series, the fifth method is called the series method. The last method solves the VIE using the functional correction technique called the variational iteration method. We introduce some examples to illustrate these methods. 

References

M. Rahman Integral equations and their applications, 2007.

S. N. Majeed Solution of Second Kind Volterra Integro Equations Using linear Non-Polynomial Spline Function.

B. Mandal and A. Chakrabarti, “Book Review Applied Singular Integral Equations (PA MARTIN),” Journal of Integral Equations and

Applications, vol. 23, no. 4, pp. 597–598, 2011.

A. M. Wazwaz Linear and nonlinear integral equations, vol. 639, 2011.

M. G. Porshokouhi, B. Ghanbari, and M. Rashidi, “Variational iteration method for solving Volterra and Fredholm integral equations of the second kind,” Gen, vol. 2, no. 1, pp. 143–148, 2011.

M. Rahman, “Numerical solutions of Volterra integral equations of second kind with the help of Chebyshev polynomials,” Annals of Pure and Applied Mathematics, vol. 1, no. 2, pp. 158–167, 2012.

A. Rawlins, “Introduction to integral equations with applications,” The Mathematical Gazette, vol. 70, no. 452, pp. 169–170, 1986.

F. Ghoreishi and M. Hadizadeh, “Numerical computation of the Tau approximation for the Volterra-Hammerstein integral equations,” Numerical Algorithms, vol. 52, no. 4, pp. 541–559, 2009.

X. Shaikh and M. Mujtaba, “Analysis of Polynomial Collocation and Uniformly Spaced Quadrature Methods for Second Kind Linear Fredholm Integral Equations-A Comparison,” Turkish Journal of Analysis and Number Theory, vol. 7, no. 4, pp. 91–97, 2019.

E. N. Houstis, W. F. Mitchell, and J. R. Rice, “Collocation software for second-order elliptic partial differential equations,” ACM Transactions on Mathematical Software (TOMS), vol. 11, no. 4, pp. 379–412, 1985.

M. M. Adhra, “Numerical Solution of Volterra Integral Equation with Delay by Using Non-Polynomial Spline Function,” Misan Journal of Academic Studies, vol. 16, no. 32, pp. 133–142, 2017.

G. Ch, “Class of Bezier,” Aided Geom, Design, vol. 20, pp. 29–39, 2003.

R. L. Burden and J. D. Faires, “Numerical analysis,” 2010.

M. Almatrafi, “Exact and numerical solutions for the GBBM equation using an adaptive moving mesh method,” Alexandria Engineering Journal, vol. 60, no. 5, pp. 4441–4450, 2021.

Z. Masouri, “Numerical expansion-iterative method for solving second kind Volterra and Fredholm integral equations using block-pulse functions,” Advanced Computational Techniques in Electromagnetics, vol. 20, pp. 7–17, 2012.

M. Zamani, “Three simple spline methods for approximation and interpolation of data,” Contemporary Engineering Sciences Journal, vol. 2, pp. 373–381, 2009.

T. Burton, “Volterra integral and differential equations(Book),” Mathematics in Science and Engineering), pp. 167–167, 1983.

Downloads

Published

2023-09-30

Issue

Section

Mathematics

How to Cite

[1]
Issa H. Al-Aidi and Ahmed Sh. Al-Atabi, “The Analytical Methods Of Volterra Integral Equations of The Second Kind”, WJCMS, vol. 2, no. 3, pp. 39–45, Sep. 2023, doi: 10.31185/wjcms.119.