The numerical solution of weakly singular integral equations based on the meshless product integration (MPI) method with error analysis

2014 ◽  
Vol 81 ◽  
pp. 76-93 ◽  
Author(s):  
Pouria Assari ◽  
Hojatollah Adibi ◽  
Mehdi Dehghan
Keyword(s):  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Product Integration ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations

scholarly journals Convergence analysis of the generalized Euler-Maclaurin quadrature rule for solving weakly singular integral equations

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1801-1815
Author(s):  
Grzegorz Rządkowski ◽  
Emran Tohidi
Keyword(s):  
Numerical Solution ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Quadrature Rule ◽  
Summation Formula ◽  
Volterra Integral Equations ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations

In the present paper we use the generalized Euler-Maclaurin summation formula to study the convergence and to solve weakly singular Fredholm and Volterra integral equations. Since these equations have different nature, the proposed convergence analysis for each equation has a different structure. Moreover, as an application of this summation formula, we consider the numerical solution of the fractional ordinary differential equations (FODEs) by transforming FODEs into the associated weakly singular Volterra integral equations of the first kind. Some numerical illustrations are designed to depict the accuracy and versatility of the idea.

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