THE NUMERICAL METHODS FOR SOLVING NONLINEAR INTEGRAL EQUATIONS

  • Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman Professor, Department of Mathematics, Faculty of Education, Omdurman Islamic University, Omdurman, Sudan
  • Marwa Eltayb Abu Elgasim Msis Department of Mathematics, Faculty of Education, Omdurman Islamic University, Omdurman, Sudan
Keywords: Nonlinear Integral Equations, Volterra Integral Equation, Fredholm Integral Equation, Numerical, Methods

Abstract

Volterra integral equations are a special type of integrative equations; they are divided into two categories referred to as the first and second type. This thesis will deal with the second type which has wide range of the applications in physics and engineering problems. The aim of this paper is to compare between analytical solution and numerical solution to solve Integral Equations. Numerical examples are presented to illustrate the applications of this methods and to compare the computed results with other numerical methods for analytical solutions. Finally by comparison of numerical results, Simplicity and efficiency of this method be shown.

Downloads

Download data is not yet available.

References

[1] Abdul-Majid Wazwaz, A First Course in Integral Equations, Second Edition, World Scientific, New Jersey, 2015. A. Jerri, Introduction to Integral Equations with Applications, Wiley, New York, (1999).
[2] A.M.Wazwaz, A First Course in Integral Equations, World Scientific, Singapore, (1997).
[3] A.M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, HEP and Springer, Beijing and Berlin, (2009). A. Jerri, Introduction to Integral Equations with Applications, Wiley, New York, (1999).
[4] A.N. Tikhonov, On the solution of incorrectly posed problem and the method of regularization, Soviet Math, 4 (1963) 1035–1038.
[5] A.M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, HEP and Springer, Beijing and Berlin, (2009).
[6] D.L. Phillips, A technique for the numerical solution of certain integral equations of the first kind, J. Asso. Comput. Mach, 9 (1962) 84–96.
[7] H.T. Davis,Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, (1962).
[8] H.T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover, Publications, New York, (1962).
[9] J. Hadamard, Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Yale University Press, New Haven, (1923).
[10] J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg., 178 (1999) 257–262.
[11] L.M. Delves and J. Walsh, Numerical Solution of Integral Equations,Oxford University Press, London, (1974).
[12] P. Linz, A simple approximation method for solving Volterra integro-differential equations of the first kind, J. Inst. Math. Appl., 14 (1974) 211–215.
[13] P. Linz, Analytical and Numerical Methods for Volterra Equations, SIAM, Philadelphia, (1985).
[14] R.K. Miller, Nonlinear Volterra Integral Equations, W.A. Benjamin, Menlo Park, CA, (1967).
[15] R. Kress, Linear Integral Equations, Springer, Berlin, (1999).
[16] R.F. Churchhouse, Handbook of Applicable Mathematics, Wiley, New York, (1981).
[17] W.E. Olmstead and R.A. Handelsman, Asymptotic solution to a class of nonlinear Volterra integral equations, II, SIAM J. Appl. Math., 30 (1976) 180–189.
[18] Y. Cherruault and V. Seng, The resolution of non-linear integral equations of the first kind using the decomposition method of Adomian, Kybernetes, 26 (1997) 109–206.
Published
2023-03-29
How to Cite
Radi, A., & Elgasim Msis, M. E. A. (2023). THE NUMERICAL METHODS FOR SOLVING NONLINEAR INTEGRAL EQUATIONS. IJRDO -JOURNAL OF MATHEMATICS, 9(3), 1-12. https://doi.org/10.53555/m.v9i3.5638