A new analytical technique to solve Volterra's integral equations

Mathematical Methods in the Applied Sciences

Volumn 34, Issue 10, 2011, Pages 1243-1253

  Vosughi, Hossein ^a   Shivanian, Elyas ^b   Abbasbandy, Saeid ^c  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b IMAM KHOMEINI INTERNATIONAL UNIVERSITY   (Iran)

^c ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Adomian decomposition method; convergence controller parameter; homotopy analysis method; linear and nonlinear Volterra integral equation

Indexed keywords

ADOMIAN DECOMPOSITION METHOD; ADOMIAN DECOMPOSITION METHODS; ANALYTICAL TECHNIQUES; CONVERGENCE-CONTROLLER PARAMETER; HIGH EFFICIENCY; HOMOTOPY ANALYSIS METHODS; NONLINEAR INTEGRAL EQUATIONS; NONLINEAR VOLTERRA INTEGRAL EQUATION; ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS; SINGULAR INTEGRAL EQUATIONS; VOLTERRA;

NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

INTEGRAL EQUATIONS;

EID: 79958780765     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.1436     Document Type: Article

References (33)

1. Liao SJ,. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Chapman & Hall/CRC Press: Boca Raton, 2003.
2. Hayat T, Javed T, Sajid M,. Analytic solution for rotating flow and heat transfer analysis of a third-grade fluid. Acta Mechanica 2007; 191: 219-229. (Pubitemid 46993923)
3. Hayat T, Khan M, Sajid M, Asghar S,. Rotating flow of a third grade fluid in a porous space with hall current. Nonlinear Dynamics 2007; 49: 83-91. (Pubitemid 46745005)
4. Sajid M, Siddiqui A, Hayat T,. Wire coating analysis using MHD Oldroyd 8-constant fluid. International Journal of Engineering Science 2007; 45: 381-392. (Pubitemid 47094796)
5. Abbasbandy S, Shivanian E,. Solution of singular linear vibrational BVPs by the homotopy analysis method. Journal of Numerical Mathematics and Stochastics 2009; 1 (1): 77-84.
6. Abbasbandy S, Shivanian E,. Prediction of multiplicity of solutions of nonlinear boundary value problems: novel application of homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation 2010; 15: 3830-3846.
7. Abbasbandy S,. Soliton solutions for the 5th-order KdV equation with the homotopy analysis method. Nonlinear Dynamics 2008; 51: 83-87. (Pubitemid 47632348)
8. Abbasbandy S,. The application of the homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation. Physics Letters A 2007; 361: 478-483.
9. Abbasbandy S, Pakdemirli M, Shivanian E,. Optimum path of a flying object with exponentially decaying density medium. Zeitschrift für Naturforschung 2009; 64a: 431-438.
10. Abbasbandy S, Shivanian E,. Series solution of the system of integro-differential equations. Zeitschrift für Naturforschung 2009; 64a: 811-818.
11. Zhu SP,. An exact and explicit solution for the valuation of American put options. Quantitative Finance 2006; 6: 229-242.
12. Zhu SP,. A closed-form analytical solution for the valuation of convertible bonds with constant dividend yield. Anziam Journal 2006; 47: 477-494.
13. Wu Y, Cheung KF,. Explicit solution to the exact Riemann problems and application in nonlinear shallow water equations. International Journal for Numerical Methods in Fluids 2008; 57 (11): 1649-1668.
14. Yamashita M, Yabushita K, Tsuboi K,. An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method. Journal of Physics A 2007; 40: 8403-8416.
15. Bouremel Y,. Explicit series solution for the Glauert-jet problem by means of the homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation 2007; 12 (5): 714-724. (Pubitemid 44942958)
16. Tao L, Song H, Chakrabarti S,. Nonlinear progressive waves in water of finite depth-an analytic approximation. Coastal Engineering 2007; 54: 825-834. (Pubitemid 47610328)
17. Song H, Tao L,. Homotopy analysis of 1D unsteady, nonlinear groundwater flow through porous media. Journal of Coastal Research 2007; 50: 292-295.
18. Molabahrami A, Khani F,. The homotopy analysis method to solve the Burgers-Huxley equation. Nonlinear Analysis B: Real World Applications 2009; 10: 589-600.
19. Bataineh AS, Noorani MSM, Hashim I,. Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method. Physics Letters A 2007; 371: 72-82.
20. Wang Z, Zou L, Zhang H,. Applying homotopy analysis method for solving differential-difference equation. Physics Letters A 2007; 369: 77-84.
21. Mustafa I,. On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy analysis method. Physics Letters A 2007; 365: 412-415.
22. Cai WH,. Nonlinear dynamics of thermal-hydraulic networks. Ph.D. Thesis, University of Notre Dame, 2006.
23. Abbasbandy S, Magyari E, Shivanian E,. The homotopy analysis method for multiple solutions of nonlinear boundary value problems. Communications in Nonlinear Science and Numerical Simulation 2009; 14: 3530-3536.
24. Kythe PK, Puri P,. Computational Methods of Linear Integral Equations. Springer: New York, 2002.
25. Baker CTH,. The Numerical Treatment of Integral Equations. Clarendon Press: Oxford, 1969.
26. Huang SC, Shaw RP,. The Trefftz method as an integral equation. Advances in Engineering Software 1995; 24: 57-63.
27. Abdou MA,. On the solution of linear and nonlinear integral equation. Applied Mathematics and Computation 2003; 146: 857-871.
28. Liang D, Zhang B,. Numerical analysis of graded mesh methods for a class of second kind integral equations on real line. Journal of Mathematical Analysis and Applications 2004; 294: 482-502. (Pubitemid 38955872)
29. Wazwaz AM,. A First Course in Integral Equations. World Scientific: NJ, 1997.
30. Babolian E, Davari A,. Numerical implementation of Adomian decomposition method for linear Volterra integral equations of the second kind. Applied Mathematics and Computation 2005; 165: 223-227. (Pubitemid 40537184)
31. Abbasbandy S,. Numerical solutions of the integral equations: homotopy perturbation method and Adomian decomposition method. Applied Mathematics and Computation 2006; 173: 493-500. (Pubitemid 43208792)
32. Abbasbandy S, Shivanian E,. A new analytical technique to solve Fredholm's integral equations. Numerical Algorithms 2011; 56: 27-43. DOI: 10.1007/s11075-010-9372-2.
33. Yves C,. Convergence of Adomian's method. Kybernetes 1989; 18 (2): 31-38.