A meshless method for the numerical solution of nonlinear weakly singular integral equations using radial basis functions

2017 ◽  
Vol 132 (5) ◽  
Author(s):  
Pouria Assari ◽  
Mehdi Dehghan
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Radial Basis Functions ◽  
Singular Integral ◽  
Meshless Method ◽  
Singular Integral Equations ◽  
Basis Functions ◽  
Weakly Singular ◽  
Radial Basis ◽  
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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