Modication of Laplace Adomian decomposition method for solving nonlinear Volterra integral and integro-dierential equations based on Newton Raphson formula

[1] J Ahmad, F Hussain, and M Naeem. Laplace decomposition method for solving
singular initial value problems. Aditi Journal of Mathematical Physics, 5:1{15, 2014.
REFERENCES 212
[2] B Ghazanfari and A Sepahvandzadeh. Adomian decomposition method for solving
Bratu's type equation. Journal of Mathematics and Computer Science, 8:236{244,
2014.
[3] D Bahuguna, A Ujlayan, and D N Pandey. A comparative study of numerical
methods for solving an integro-dierential equation. Computers and Mathematics
with Applications, 57:1485{1493, 2009.
[4] N Bildik and M Inc. A comparison between Adomian decomposition and Tau
methods. Abstract and Applied Analysis, 2013:1{5, 2013.
[5] J A S Cano. Adomian decomposition method and Taylor series method in ordinary
dierential equations. International Journal of Research and Reviews in Applied
Sciences, 16:168{175, 2013.
[6] N Doan. Solution of the system of ordinary dierential equations by combined Laplace
transform Adomian decomposition method. Mathematical and Computational
Applications, 17:203{211, 2012.
[7] D J Evans and K R Raslan. The Adomian decomposition method for solving delay
dierential equation. International Journal of Computer Mathematics, 00:1{6, 2004.
[8] J Fadaei. Application of Laplace Adomian decomposition method on linear and
nonlinear system of PDEs. Applied Mathematical Sciences, 5:1307{1315, 2011.
[9] F A Hendi. Laplace Adomian decomposition method for solving the nonlinear Volterra
integral equation with weakly kernels. Studies in Nonlinear Sciences, 2:129{134, 2011.
[10] S Islam, Y Khan, N Faraz, and F Austin. Numerical solution of logistic dierential
equations by using Laplace decomposition method. World Applied Sciences Journal,
8:1100{1105, 2010.
[11] H Jafari, M Ghorbani, and S Ghasempour. A note on exact solutions for nonlinear
integral equations by a modied homotopy perturbation method. New Trends in
Mathematical Sciences, 2:22{26, 2013.
[12] A V Kamyad, M Mehrabinezhad, and J S Nadja. A numerical approach for solving
linear and nonlinear Volterra integral equations with controlled error. International
Journal of Applied Mathematics, 40:1{6, 2010.
[13] M Khan, M Hussain, H Jafari, and Y Khan. Application of Laplace decomposition
method to solve nonlinear coupled partial dierential equations. World Applied
Sciences Journal, 9:13{19, 2010.
[14] S A Khuri. A Laplace decomposition algorithm applied to a class of nonlinear
dierential equation. Journal of Applied Mathematics, 1:141{155, 2001.
REFERENCES 213
[15] M A Koroma, S Widatalla, A F Kamara, and C Zhang. Laplace Adomian
decomposition method applied to a two-dimensional viscous
ow with shrinking sheet.
7:525{529, 2013.
[16] A Kumar and R D Pankaj. Laplace decomposition method to study solitary wave
solutions of coupled nonlinear partial dierential equation. ISRN Computational
Mathematics, 2012:1{5, 2012.
[17] Y Lin and C K Chen. Modied Adomian decomposition method for double singular
boundary value problems. Romanian Journal of Physics, 59:443{453, 2014.
[18] K Maleknejad and E Naja. Numerical solution of nonlinear Volterra integral
equations using the idea of quasilinearization. Communication in Nonlinear Science
and Numerical Simulation, 16:93{100, 2011.
[19] J Manaanheris. Solving the integro-dierential equations using the modied Laplace
Adomian decomposition method. Journal of Mathematical Extension, 6:41{55, 2012.
[20] M A Mohamed and M S Torky. Numerical solution of nonlinear system of
partial dierential equations by the Laplace decomposition method and the Pade
approximation. American Journal of Computational Mathematics, 3:175{184, 2013.
[21] L Saeedi, A Tari, and S H Momeni Masuleh. Numerical solution of a class of the
nonlinear Volterra integro-dierential equations. Journal of Applied Mathmatics and
Informatics, 31:65{77, 2013.
[22] N Singh and M Kumar. Adomian decomposition method for solving higher order
boundary value problems. Mathematical Theory and Modeling, 2:11{22, 2011.
[23] A H Waleed. Solving nth-order integro-dierential equations using the combined
Laplace transform-Adomian decomposition method. Applied Mathematics, 4:882{
886, 2013.
[24] A M Wazwaz. The combined Laplace transform-Adomian demcomposition method
for handling nonlinear Volterra integro-dierential equations. Applied Mathematics
and Computation, 216:1304{1309, 2010.
[25] A M Wazwaz. Linear and Nonlinear Integral Equations: Methods and Applications.
Springer, 2011.
[26] S P Yan, H Jafari, and H K Jassim. Local fractional Adomian decomposition
and function decomposition methods for Laplace equation within local fractional
operators. Advances in Mathematical Physics, 2014:1{7, 2014.
[27] C Yang and J Hou. An approximate solution of nonlinear fractional dierential
equation by Laplace transform and Adomian polynomials. Journal of Information
and Computational Science, 10:213{222, 2013.
REFERENCES 214
[28] F K Yin, W Y Han, and J Q Song. Modied Laplace decomposition method for
Lane-Emden type dierential equations. International Journal of Applied Physics
and Mathematics, 3:98{102, 2013.
[29] J B Yindoula, P Youssouf, G Bissanga, F Bassono, and B Some. Application
of the Adomian decomposition method and Laplace transform method to solving
the convection diusion-dissipation equation. International Journal of Applied
Mathematical Research, 3:30{35, 2014.