Monotone iterative sequences for nonlinear integro-differential equations of second order

Nonlinear Analysis: Real World Applications

Volumn 12, Issue 6, 2011, Pages 3665-3673

  Al Mdallal, Qasem M ^a  

^a UNITED ARAB EMIRATES UNIVERSITY   (United Arab Emirates)

Author keywords

Lower and upper solutions; Maximum principle; Monotone method; Nonlinear integro differential equations

Indexed keywords

A-MONOTONE; EFFICIENT ALGORITHM; ITERATIVE SEQUENCES; LOWER AND UPPER SOLUTION; MONOTONE METHOD; MONOTONE SEQUENCES; NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS; NUMERICAL RESULTS; SECOND ORDERS; UNIFORMLY CONVERGENT; UPPER AND LOWER SOLUTIONS;

ALGORITHMS; DIFFERENTIATION (CALCULUS); INTEGRODIFFERENTIAL EQUATIONS; NONLINEAR EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 80052022098     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.06.023     Document Type: Article

References (18)

1. R.P. Agarwal Boundary value problems for higher order integro-differential equations Nonlinear Anal. 7 1983 259 270
2. R.P. Agarwal Boundary Value Problems for High Ordinary Differential Equations 1986 World Scientific Singapore
3. A. Wazwaz A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations Appl. Math. Comput. 181 2006 1703 1712 (Pubitemid 44646640)
4. K. Maleknejad, and M. Hadizadeh A new computational method for VolterraFredholm integral equations J. Comput. Appl. Math. 37 1999 1 8
5. D. Contea, and I. Preteb Fast collocation methods for Volterra integral equations of convolution type J. Comput. Appl. Math. 196 2006 652 663
6. J. Saberi-Nadja, and A. Ghorbani Hes homotopy perturbation method: An effective tool for solving nonlinear integral and integro-differential equations Comput. Math. Appl. 58 2009 2379 2390
7. H. Brunner On the numerical solution of nonlinear Volterra integro-differential equations BIT 13 1973 381 390
8. H. Brunner On the numerical solution of nonlinear VolterraFredholm integral equation by collocation methods SIAM J. Numer. Anal. 27 4 1990 987 1000 (Pubitemid 20710868)
9. O. Lepik Haar wavelet method for nonlinear integro-differential equations Appl. Math. Comput. 176 2006 324 333
10. G. Ebadi, M. Rahimi-Ardabili, and S. Shahmorad Numerical solution of the nonlinear Volterra integro-differential equations by the Tau method Appl. Math. Comput. 188 2007 1580 1586 (Pubitemid 46710047)
11. K. Maleknejad, and Y. Mahmoudi Taylor polynomial solution of high-order nonlinear Volterra Fredholm integro-differential equations Appl. Math. Comput. 145 2003 641 653
12. P. Darania, and K. Ivaz Numerical solution of nonlinear VolterraFredholm integro-differential equations Comput. Math. Appl. 56 2008 2197 2209
13. A.M. Wazwaz The combined Laplace transformAdomian decomposition method for handling nonlinear Volterra integro-differential equations Appl. Math. Comput. 216 2010 1304 1309
14. E. Liz, and Juan J. Nieto Boundary value problems for second order integro-differential equations of Fredholm type 1 J. Comput. Appl. Math. 72 1996 215 225 (Pubitemid 126380094)
15. M.H. Protter, and H.F. Weinberger Maximum Principles in Differential Equations 1984 Springer-Verlag New York
16. M. Al-Refai, M. Syam, and Q.M. Al-Mdallal Analytical sequences of upper and lower solutions for a class of elliptic equations J. Math. Anal. Appl. 374 2011 402 411
17. M. Al-Refai Existence, uniqueness and bounds for a problem in combustion theory J. Comput. Appl. Math. 167 2004 255 269 (Pubitemid 38653521)
18. R.G. Bartle, and D.R. Sherbert Introduction to Real Analysis 3rd ed. 2000 John Wiley and Son New York