Numerical solution of the general form linear Fredholm-Volterra integro-differential equations by the Tau method with an error estimation

The Tau method, produces approximate polynomial solutions of differential, integral and integro-differential equations. In this paper extension of the Tau method has been done for the numerical solution of the general form of linear Fredholm-Volterra integro-differential equations. An efficient error estimation for the Tau method is also introduced. Details of the method are presented and some numerical results along with estimated errors are given to clarify the method and its error estimator.

[1]  D. Gottlieb,et al.  Numerical analysis of spectral methods : theory and applications , 1977 .

[2]  K. M. Liu,et al.  Numerical solution of eigenvalue problems for partial differential equations with the Tau-lines method , 1986 .

[3]  H. G. Khajah,et al.  Iterated solutions of linear operator equations with the Tau method , 1997, Math. Comput..

[4]  Eduardo L. Ortiz,et al.  The Tau Method , 1969 .

[5]  Mehmet Sezer,et al.  The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials , 2000, Appl. Math. Comput..

[6]  Eduardo L. Ortiz,et al.  An operational approach to the Tau method for the numerical solution of non-linear differential equations , 1981, Computing.

[7]  H. Samara,et al.  Numerical solution of partial differential equations with variable coefficients with an operational approach to the tau method , 1984 .

[8]  E. Ortiz,et al.  Numerical solution of nonlinear partial differential equations with the Tau method , 1985 .

[9]  Eduardo L. Ortiz,et al.  Numerical solution of differential eigenvalue problems with an operational approach to the Tau method , 2005, Computing.

[10]  A. Makroglou.  Convergence of a block-by-block method for nonlinear Volterra integro-differential equations , 1980 .

[11]  K. Liu,et al.  Tau method approximation of differential eigenvalue problems where the spectral parameter enters nonlinearly , 1987 .

[12]  Kam-Moon Liu,et al.  Numerical solution of ordinary and partial functional-differential eigenvalue problems with the Tau Method , 2005, Computing.

[13]  E. Ortiz,et al.  A bidimensional tau-elements method for the numerical solution of nonlinear partial differential equations with an application to burgers' equation , 1986 .

[14]  Eduardo L. Ortiz,et al.  Approximation of eigenvalues defined by ordinary differential equations with the Tau method , 1983 .