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M. Hosseini AliAbadi,S. Shahmorad 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.9 No.2
In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach. In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.
Aliabadi, M.-Hosseini,Shahmorad, S. 한국전산응용수학회 2002 The Korean journal of computational & applied math Vol.9 No.2
In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.
THE BUCHSTAB'S FUNCTION AND THE OPERATIONAL TAU METHOD
Aliabadi, M.Hosseini 한국전산응용수학회 2000 The Korean journal of computational & applied math Vol.7 No.3
In this article we discuss some aspects of operational Tau Method on delay differential equations and then we apply this method on the differential delay equation defined by $\omega(u)\;=\frac{1}{u}\;for\;1\lequ\leq2$ and $(u\omega(u))'\;=\omega(u-1)\;foru\geq2$, which was introduced by Buchstab. As Khajah et al.[1] applied the Recursive Tau Method on this problem, they had to apply that Method under the Mathematica software to get reasonable accuracy. We present very good results obtained just by applying the Operational Tau Method using a Fortran code. The results show that we can obtain as much accuracy as is allowed by the Fortran compiler and the machine-limitations. The easy applications and reported results concerning the Operational Tau are again confirming the numerical capabilities of this Method to handle problems in different applications.