TY - JOUR
T1 - Application of Tau Approach for Solving Integro-Differential Equations with a Weakly Singular Kernel
TT -
JF - IJMSI
JO - IJMSI
VL - 16
IS - 1
UR - http://ijmsi.ir/article-1-1266-en.html
Y1 - 2021
SP - 145
EP - 168
KW - Shifted Legendre tau method
KW - Weakly singular kernel
KW - Integro-differential equation
KW - Convection-diffusion equation.
N2 - In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices. Also the convergence analysis for shifted Legendre polynomials and error estimation for tau method have been discussed and approved with the exact solution. Finally, several numerical examples are given to demonstrate the high accuracy of the method.
M3
ER -