Chitkara University Publications

Application of Combine Natural Transform and Adomian Decomposition Method in Volterra Integro-Differential Equations

Abstract:

In this paper we introduced the combine Natural transform and Adomian decomposition method to solve the nonlinear voltrra integro-differential equations of first kind and second kind.To illustrate the method some examples are solved by using the above said method.

Author(s):

  • A.D. Chindhe, Balbhim College, Beed, Maharashtra, India
  • S.B. Kiwne, Deogiri College, Aurangabad, Maharashtra, India

DOI: 

Keywords: 

Volterra Integro-Differential Equations, Laplace Transform, Natural transform, Adomian Decomposition Method

References:

A.J. Jerri, Introduction to Integral Equations with Applications, Wiley, New York, 1999.

A.M. Wazwaz, A First Course in Integral Equations, World Scientific, Singapore, 1997. https://doi.org/10.1142/3444

A.M. Wazwaz, The combined Laplace transform–Adomian decomposition method for handling nonlinear Volterra integrodifferential equations, Applied Mathematics and Computation, 216, pp 1304–1309, 2010.https://doi.org/10.1016/j.amc.2010.02.023

Belgacem, F. B. M and Silambarasan R., Theory of the Natural transform, Mathematics in Engg Sci and Aerospace (MESA) journal, Vol. 3, No. 1, pp99–124, 2012.

Joel.L.Schiff. Laplace transform Theory and Applications. Auckland,New-Zealand.Springer-2005.

Loonker Deshna and Banerji P.K., application of Natural transform to differential equations, J. Indian Acad Math., 35(1), pp 151–158, 2013.

Loonker Deshna and Banerji P.K., Natural transform for distribution and Boehmian spaces, Math.Engg.Sci.Aerospace, 4(1), pp 69–76, 2013.

L. Debnath and D.Bhatta.Integral Transforms and their applications. 2ndedition.C.R.C.Press. London.2007.

M.R.Spiegel.Theory and Problems of Laplace Transforms. Schaums Outline Series, McGraw-Hill, New York, 1965.

R. Kanwal, Linear Integral Equations, Birkhauser, Berlin, 1997.https://doi.org/10.1007/978-1-4612-0765-8

Silambarasan, R. and Belgacem, F. B. M., Advances in the Natural transform, 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences AIP Conf. Proc., 1493, 106–110, 2012.

Silambarasan, R. and Belgacem, F. B. M, Applications of the Natural transform to Maxwell’s Equations, PIERS Suzhou, China, Sept 12-16, pp 899–902, 2011.

Z.H.Khan and W.A.Khan.N-transform properties and applications. NUST Jour of Engg Sciences., 1(1) pp 127–133, 2008.

 

 

0 0 votes
Article Rating
Subscribe
Notify of
0 Comments
Inline Feedbacks
View all comments
CHITKARA UNIVERSITY ADMINISTRATIVE OFFICE SARASWATI KENDRA, PO Box No. 70 SCO – 160-161,Sector – 9C, Chandigarh – 160009, India. +91-172-2741000, +91-172-4691800 chitkarauniversitypublications@chitkara.edu.in

    0
    Would love your thoughts, please comment.x
    ()
    x