In this paper we introduce a new approach for numerical solution of nonlinear Volterra integral equation of second kinds. This numerical solution is based on the Laplace transform and Adomian Decomposition Method by using He's polynomials. Then comparative study is made on the exact solution, approximate solution and estimated error.
All calculations are made by Matlab 13 Version and illustrated by example.
You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.
References
[1] A.M.Wazwaz, A First Course in Integral Equations, World Scientific, London, 2015.
[2] N. Ahmad and B.M. Singh, Numerical solution of integral equation using
Galerkin mehod with Hermite, Chebyshev and orthogonal polynomials,
Journal of Science and Arts, 1, No 50 (2020), 35-42.
[3] H. Ahmad, F. Hussain and M. Naeem, Laplace decomposition method
for solving singular initial value problems, Aditi Journal of Mathematical
Physics, 5 (2014), 1-15.
[4] A. Abbasbandy, Numerical solution of integral equation: Homotopy perturbation method and Adomian decomposition method, Appl. Math. Comput.
, 173, No 2-3 (2006), 493-500.
[5] D. Rani and V. Mishra, Modification of Laplace Adomian decomposition method for solving nonlinear Volterra integral and integro-differential
equation based on Newton Raphson formula, Eur. Journal of Pure and
Appl. Mathematics, 11, No 1 (2018), 202-214.
[6] S.P. Yan, H. Jafari and H.K. Jassim, Local fractional Adomian decomposition method and function decomposition methods for Laplace equation
within local fractional operators, Advances in Mathematical Physics, 2014
(2014), 1-7.
[7] Y. Lin and C. K. Chen, Modified Adomian decomposition method for
double singular boundary value problems, Romanian Journal of Physics,
59 (2014), 443-453.
[8] A.M. Waswas, Linear and Nonlinear Integral Equations, Method and Applications
, Springer, 2011.
[9] R.H. Khan and H.O. Bakodah, Adomian decomposition method and its
modification for nonlinear Abel’s integral equations, Int. Journal of Math.
Analysis, 7, No 48 (2013), 2349-2358.
[10] A.J. Jerri, Introduction to Integral Equation with Application, Second Ed.,
John Wiley and Sons, 1999.
[11] K.E. Atkinson, The Numerical Solution of Integral Equations of the Second
Kind, Cambridge University Press, England, 1997.