Hybrid Legendre polynomials and Block-Pulse functions approach for nonlinear Volterra-Fredholm integro-differential equations

This paper introduces an approach for obtaining the numerical solution of the nonlinear Volterra-Fredholm integro-differential (NVFID) equations using hybrid Legendre polynomials and Block-Pulse functions. These hybrid functions and their operational matrices are used for representing matrix form of these equations. The main characteristic of this approach is that it reduces NVFID equations to a system of algebraic equations, which greatly simplifying the problem. Numerical examples illustrate the validity and applicability of the proposed method.

[1]  Mohsen Razzaghi,et al.  HYBRID FUNCTIONS APPROACH FOR LINEARLY CONSTRAINED QUADRATIC OPTIMAL CONTROL PROBLEMS , 2003 .

[2]  Mohsen Razzaghi,et al.  Numerical solution of the controlled Duffing oscillator by hybrid functions , 2003, Appl. Math. Comput..

[3]  M. Abdou,et al.  On a symptotic methods for Fredholm--Volterra integral equation of the second kind in contact problems , 2003 .

[4]  Maw-Ling Wang,et al.  Shifted Legendre direct method for variational problems , 1983 .

[5]  Zdzislaw Jackiewicz,et al.  Stochastic approximations of perturbed Fredholm Volterra integro-differential equation arising in mathematical neurosciences , 2007, Appl. Math. Comput..

[6]  Carlo Cattani,et al.  Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kind , 2010, Appl. Math. Comput..

[7]  Khosrow Maleknejad,et al.  Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations , 2003, Appl. Math. Comput..

[8]  Khosrow Maleknejad,et al.  Numerical solution of integral equations system of the second kind by Block-Pulse functions , 2005, Appl. Math. Comput..

[9]  L. Delves,et al.  Computational methods for integral equations: Frontmatter , 1985 .

[10]  Esmail Babolian,et al.  Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions , 2009, Comput. Math. Appl..

[11]  M. Abdou,et al.  Integral equation of mixed type and integrals of orthogonal polynomials , 2002 .

[12]  Chun-Hui Hsiao,et al.  Hybrid function method for solving Fredholm and Volterra integral equations of the second kind , 2009 .

[13]  Khosrow Maleknejad,et al.  Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functions , 2004, Appl. Math. Comput..

[14]  Khosrow Maleknejad,et al.  Solving linear integro-differential equation system by Galerkin methods with hybrid functions , 2004, Appl. Math. Comput..

[15]  Chun-Hui Hsiao,et al.  Numerical solutions of linear time-varying descriptor systems via hybrid functions , 2010, Appl. Math. Comput..

[16]  C. Cattani.  Shannon Wavelets for the Solution of Integrodifferential Equations , 2010 .

[17]  A. Wazwaz.  A First Course in Integral Equations , 1997 .

[18]  Abdul-Majid Wazwaz,et al.  The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro-differential equations , 2010, Appl. Math. Comput..