STWS approach for Hammerstein system of nonlinear Volterra integral equations of the second kind

ABSTRACT In this paper, single-term Walsh series (STWS) method is applied to obtain the numerical solutions of Hammerstein systems of nonlinear Volterra integral equations of second kind (HSNVIES). Using the properties of the STWS method, HSNVIES can be easily converted into solvable recursive system of algebraic equations. Solutions obtained from the recursive system of algebraic equations are the solutions of the HSNVIES. Illustrative examples are provided with numerical solutions and the efficiency of this STWS method is also compared with the existing methods.

[1]  Jafar Biazar,et al.  Application of homotopy perturbation method for systems of Volterra integral equations of the first kind , 2009 .

[2]  M. Khumalo,et al.  Numerical Solutions of a Class of Nonlinear Volterra Integral Equations , 2014 .

[3]  Mohsen Razzaghi,et al.  Solution of nonlinear Volterra-Hammerstein integral equations via single-term Walsh series method , 2005 .

[5]  Khosrow Maleknejad,et al.  Using Runge-Kutta method for numerical solution of the system of Volterra integral equation , 2004, Appl. Math. Comput..

[6]  K. Murugesan,et al.  System of linear second order Volterra integro-differential equations using Single Term Walsh Series technique , 2016, Appl. Math. Comput..

[7]  Mohsen Rabbani,et al.  Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method , 2007, Appl. Math. Comput..

[8]  F. Castro,et al.  Solvability of Systems of Polynomial Equations with Some Prescribed Monomials , 2009 .

[9]  Jafar Biazar,et al.  He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind , 2009 .

[10]  G. Rao.  Piecewise Constant Orthogonal Functions and Their Application to Systems and Control , 1983 .

[11]  K. Murugesan,et al.  Method of Solving Linear System of Volterra Integro-Differential Equations Using the Single Term Walsh Series , 2017 .

[12]  Esmail Babolian,et al.  Restarted Adomian method for system of nonlinear Volterra integral equations , 2005, Appl. Math. Comput..

[14]  Jafar Biazar,et al.  Chebyshev wavelets approach for nonlinear systems of Volterra integral equations , 2012, Comput. Math. Appl..

[15]  Khosrow Maleknejad,et al.  Application of 2D-BPFs to nonlinear integral equations , 2010 .

[16]  P. Catană.  SOLVABILITY OF NONLINEAR EQUATIONS , 2008 .

[17]  Adi Ben-Israel.  A Newton-Raphson method for the solution of systems of equations , 1966 .

[18]  A. Shidfar,et al.  Solving a system of integral equations by an analytic method , 2011, Math. Comput. Model..

[19]  Behnam Sepehrian.  Single-term Walsh series method for solving Volterra's population model , 2014 .

[20]  Mohsen Razzaghi,et al.  Solution of time-varying singular nonlinear systems by single-term Walsh series , 2003 .

[21]  K. R. Palanisamy,et al.  Analysis and optimal control of linear systems via single term Walsh series approach , 1981 .

[22]  Sedaghat Shahmorad,et al.  Block by block method for the systems of nonlinear Volterra integral equations , 2010 .

[23]  P. Sannuti,et al.  Analysis and synthesis of dynamic systems via block-pulse functions , 1977 .

[24]  Abdul-Majid Wazwaz,et al.  The modified decomposition method for analytic treatment of non-linear integral equations and systems of non-linear integral equations , 2005, Int. J. Comput. Math..

[25]  Mohsen Razzaghi,et al.  SINGLE-TERM WALSH SERIES METHOD FOR THE VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS , 2004 .

[26]  C. G. Broyden.  A New Method of Solving Nonlinear Simultaneous Equations , 1969, Comput. J..

[27]  K Murugesan.  Analysis of singular systems using the single term walsh series technique , 1991 .

[28]  Elçin Yusufoglu,et al.  A homotopy perturbation algorithm to solve a system of Fredholm-Volterra type integral equations , 2008, Math. Comput. Model..

[29]  V. Balakumar,et al.  Single-Term Walsh Series method for systems of linear Volterra integral equations of the second kind , 2014, Appl. Math. Comput..

[30]  T. Srinivasan,et al.  Extension of computation beyond the limit of initial normal interval in Walsh series analysis of dynamical systems , 1980 .

[31]  Musa A. Mammadov,et al.  Solving a system of nonlinear integral equations by an RBF network , 2009, Comput. Math. Appl..

[32]  H. Marasi,et al.  Block-pulse functions approach to numerical solution of Abel’s integral equation , 2015 .

[33]  Esmail Babolian,et al.  A numerical method for solving systems of linear and nonlinear integral equations of the second kind by hat basis functions , 2011, Comput. Math. Appl..