A matrix formulation of the Tau Method for Fredholm and Volterra linear integro-differential equations

2002 ◽  
Vol 9 (2) ◽  
pp. 497-507 ◽  
Author(s):  
M. Hosseini AliAbadi ◽  
S. Shahmorad
Keyword(s):  
Differential Equations ◽  
Tau Method ◽  
Matrix Formulation

scholarly journals A Comparison between Adomian Decomposition and Tau Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Necdet Bildik ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Tau Method ◽  
Adomian Decomposition

We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.

A Comparative Study of Integer and Noninteger Order Wavelets for Fractional Nonlinear Fredholm Integro-Differential Equations

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
F. Mohammadi ◽  
J. A. Tenreiro Machado
Keyword(s):  
Differential Equations ◽  
Comparative Study ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Efficient Algorithm ◽  
Operational Matrix ◽  
Tau Method ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
Integer Order

This paper compares the performance of Legendre wavelets (LWs) with integer and noninteger orders for solving fractional nonlinear Fredholm integro-differential equations (FNFIDEs). The generalized fractional-order Legendre wavelets (FLWs) are formulated and the operational matrix of fractional derivative in the Caputo sense is obtained. Based on the FLWs, the operational matrix and the Tau method an efficient algorithm is developed for FNFIDEs. The FLWs basis leads to more efficient and accurate solutions of the FNFIDE than the integer-order Legendre wavelets. Numerical examples confirm the superior accuracy of the proposed method.

Numerical solution of the nonlinear Volterra integro-differential equations by the Tau method

2007 ◽  
Vol 188 (2) ◽  
pp. 1580-1586 ◽  
Author(s):  
G. Ebadi ◽  
M.Y. Rahimi-Ardabili ◽  
S. Shahmorad
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Tau Method

Numerical solution of Volterra integro-differential equations by the Tau method with the Chebyshev and Legendre bases

2005 ◽  
Vol 170 (1) ◽  
pp. 314-338 ◽  
Author(s):  
J. Pour-Mahmoud ◽  
M.Y. Rahimi-Ardabili ◽  
S. Shahmorad
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Tau Method
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