A new homotopy perturbation method for system of nonlinear integro-differential equations

References

• Abbasbandy, S. , 2006. Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method , Appl. Math. Comput. 173 (2006), pp. 493–500.
   Web of Science ®Google Scholar
• Beléndez, A. , Beléndez, T. , Márquez, A. , and Neipp, C. , 2008. Application of He's homotopy perturbation method to conservative truly nonlinear oscillators , Chaos Solitons Fractals 37 (2) (2008), pp. 770–780.
   Web of Science ®Google Scholar
• Biazar, J. , and Ghazvini, H. , 2007. Exact solutions for nonlinear Schrödinger equations by He's homotopy perturbation method , Phys. Lett. A 366 (2007), pp. 79–84.
   Web of Science ®Google Scholar
• Biazar, J. , and Ghazvini, H. , 2008. Numerical solution for special non-linear Fredholm integral equation by HPM , Appl. Math. Comput. 195 (2008), pp. 681–687.
   Web of Science ®Google Scholar
• Biazar, J. , and Ghazvini, H. , 2009. He's homotopy perturbation method for solving system of Volterra integral equations of the second kind , Chaos Solitons Fractals 39 (2009), pp. 770–777.
   Web of Science ®Google Scholar
• Biazar, J. , and Ghazvini, H. , 2009. A new technique for solving integral-differential equations , Comput. Math. Appl. 58 (11–12) (2009), pp. 2084–2090.
   Web of Science ®Google Scholar
• Biazar, J. , Ghazvini, H. , and Eslami, M. , 2009. He's homotopy perturbation method for systems of integro-differential equations , Chaos Solitons Fractals 39 (2009), pp. 1253–1258.
   Web of Science ®Google Scholar
• Brunner, H. , 2004. Collocation Method for Volterra Integral and Related Functional Equations . MA. Cambridge: Cambridge University Press; 2004, Cambridge Monograph on Applied and Computational Mathematics.
   Google Scholar
• Dehghan, M. , and Shakeri, F. , 2008. Use of He's homotpy perturbation method for solving a partial differential equation arising in modeling of flow in porous media, , J. Porous Media 11 (2008), pp. 765–778.
   Web of Science ®Google Scholar
• Dehghan, M. , and Shakeri, F. , 2008. Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method , Prog. Electromagn. Res. 78 (2008), pp. 361–376.
   Web of Science ®Google Scholar
• Dehghan, M. , and Shakeri, F. , 2007. Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method , Phys. Scripta 75 (2007), pp. 778–787.
   Web of Science ®Google Scholar
• El Doma, M. , 1987. Analysis of nonlinear integro differential equations arising in age-dependent epidemic models , Nonlinear Anal. Theory Methods Appl 11 (8) (1987), pp. 913–937.
   Web of Science ®Google Scholar
• Ganji, D. D. , and Sadigh, A. , 2006. Application of He's homotopy-perturbation method to nonlinear coupled systems of Reaction-diffusion equations , Int. J. Nonlinear Sci. Numer. Simul 7 (3) (2006), pp. 411–418.
   Web of Science ®Google Scholar
• Ganji, D. D. , and Rafei, M. , 2006. Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation by homotopy perturbation method , Phys. Lett. A 356 (2006), pp. 131–137.
   Web of Science ®Google Scholar
• Golbabai, A. , and Javidi, M. , 2007. Application of homotopy perturbation method for solving eighth-order boundary value problems , Appl. Math. Comput 191 (1) (2007), pp. 334–346.
   Web of Science ®Google Scholar
• Golbabai, A. , and Javidi, M. , 2007. Application of He's homotopy perturbation method for nth-order integro-differential equations , Appl. Math. Comput. 190 (2007), pp. 1409–1416.
   Web of Science ®Google Scholar
• He, J. H. , 1999. Homotopy perturbation technique , Comput. Methods Appl. Mech. Engrg. 178 (1999), pp. 257–262.
   Web of Science ®Google Scholar
• He, J. H. , 2003. A coupling method of homotopy technique and perturbation technique for nonlinear problems , Int. J. Non-Linear Mech 35 (1) (2003), pp. 7–43.
   Google Scholar
• He, J. H. , 2004. Comparison of homotopy perturbation method and homotopy analysis method, , Appl. Math. Comput. 156 (2004), pp. 527–539.
   Web of Science ®Google Scholar
• He, J. H. , 2003. Homotopy perturbation method: a new nonlinear analytical technique , Appl. Math. Comput. 135 (2003), pp. 73–79.
   Web of Science ®Google Scholar
• He, J. H. , 2006. Some asymptotic methods for strongly nonlinear equations , Int. J. Modern Phys. B 20 (2006), pp. 1141–1199.
   Web of Science ®Google Scholar
• Odibat, Z. , and Momani, S. , 2007. Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order , Chaos Solitons Fractals 36 (2007), pp. 167–174.
   Web of Science ®Google Scholar
• Saadatmandi, A. , Dehghan, M. , and Eftekhari, A. , 2009. Application of He's homotopy perturbation method for non-linear system of second-order boundary value problems , Nonlinear Anal. Real World Appl. 10 (2009), pp. 1912–1922.
   Web of Science ®Google Scholar
• Siddiqui, A. M. , Mahmood, R. , and Ghori, G. K. , 2006. Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder , Phys. Lett.A 352 (2006), pp. 404–410.
   Web of Science ®Google Scholar
• Soltanian, F. , Dehghan, M. , and Karbassi, S. M. , 2009. Solution of the differential-algebraic equations via homotopy perturbation method and their engineering applications , Int. J. Comput. Math. (2009).
   Web of Science ®Google Scholar
• Tamizhmani, K. M. , Satsuma, J. , Grammaticos, B. , and Ramani, V. , 1999. Nonlinear integro differential equations as a discreet systems , Inverse Probl. 15 (1999), pp. 787–791.
   Web of Science ®Google Scholar