New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations

In this paper, recently developed perturbation iteration method is used to solve Fredholm and Volterra integral equations. The study shows that the new method can be applied to both types of integral equations. Some numerical examples are given, and results are compared with other studies to illustrate the efficiency of the method.

[1]  Ji-Huan He,et al.  Nonlinear oscillator with discontinuity by parameter-expansion method , 2008 .

[2]  H. Hu,et al.  OSCILLATIONS IN AN x(2m+2)/(2n+1) POTENTIAL , 2003 .

[3]  Hakan Boyaci,et al.  Generation of root finding algorithms via perturbation theory and some formulas , 2007, Appl. Math. Comput..

[4]  Ronald E. Mickens,et al.  A generalized iteration procedure for calculating approximations to periodic solutions of “truly nonlinear oscillators” , 2005 .

[5]  Ronald E. Mickens.  Iteration method solutions for conservative and limit-cycle x1/3 force oscillators , 2006 .

[6]  A Root-Finding Algorithm with Fifth Order Derivatives , 2008 .

[7]  M. Pakdemirli,et al.  A New Perturbation-Iteration Approach for First Order Differential Equations , 2011 .

[8]  Sehar Iqbal,et al.  Application of optimal homotopy asymptotic method for the analytic solution of singular Lane-Emden type equation , 2011, Appl. Math. Comput..

[9]  Ji-Huan He,et al.  Iteration Perturbation Method for Strongly Nonlinear Oscillations , 2001 .

[10]  Ji-Huan He,et al.  Homotopy Perturbation Method with an Auxiliary Term , 2012 .

[11]  Frank C. Hoppensteadt,et al.  Random Perturbation Methods with Applications in Science and Engineering , 2002 .

[12]  R. Mickens,et al.  GENERALIZED HARMONIC BALANCE/NUMERICAL METHOD FOR DETERMINING ANALYTICAL APPROXIMATIONS TO THE PERIODIC SOLUTIONS OF THE x4/3 POTENTIAL , 2002 .

[13]  S. Abbasbandy,et al.  New perturbation‐iteration solutions for nonlinear heat transfer equations , 2012 .

[14]  Vimal Singh,et al.  Perturbation methods , 1991 .

[15]  D. Jordan,et al.  Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers , 1979 .

[16]  Ronald E. Mickens,et al.  Iteration procedure for determining approximate solutions to non-linear oscillator equations , 1987 .

[17]  Mehmet Pakdemirli,et al.  New perturbation-iteration solutions for Bratu-type equations , 2010, Comput. Math. Appl..

[18]  H. A. Yurtsever,et al.  Perturbative Derivation and Comparisons of Root-Finding Algorithms with Fourth Order Derivatives , 2007 .

[19]  Abdul Majeed Siddiqui,et al.  Some solutions of the linear and nonlinear Klein-Gordon equations using the optimal homotopy asymptotic method , 2010, Appl. Math. Comput..