scholarly journals Extrapolation and Splitting Extrapolation Algorithm for Multidimensional Weakly Singular Integral of Product Type

IEEE Access ◽  
2017 ◽  
Vol 5 ◽  
pp. 10506-10514 ◽  
Author(s):  
Yubin Pan ◽  
Jin Huang
Keyword(s):  
Singular Integral ◽  
Product Type ◽  
Extrapolation Algorithm ◽  
Weakly Singular ◽  
Splitting Extrapolation

scholarly journals On multi-singular integral equations involving n weakly singular kernels

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1323-1333 ◽  
Author(s):  
Sales Nabavi ◽  
O. Baghani
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Singular Integral ◽  
Applied Mathematics ◽  
Uniform Space ◽  
Singular Integral Equations ◽  
Restrictive Assumption ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Kernels

We deal with some sources of Banach spaces which are closely related to an important issue in applied mathematics i.e. the problem of existence and uniqueness of the solution for the very applicable weakly singular integral equations. In the classical mode, the uniform space (C[a,b], ||.||?) is usually applied to the related discussion. Here, we apply some new types of Banach spaces, in order to extend the area of problems we could discuss. We consider a very general type of singular integral equations involving n weakly singular kernels, for an arbitrary natural number n, without any restrictive assumption of differentiability or even continuity on engaged functions. We show that in appropriate conditions the following multi-singular integral equation of weakly singular type has got exactly a solution in a defined Banach space x(t) = ?p,i=1 ?i/?(^?i) ?t,0 fi(s,x(s)) (tn-tn-1)1-?i,n...(t1-s)1-?i,1 dt + ?(t). In particular we consider the famous fractional Langevin equation and by the method we could extend the region of variations of parameter ?+ ? from interval [0,1) in the earlier works to interval [0,2).

scholarly journals Cubic Spline Approximation for Weakly Singular Integral Models

2013 ◽  
Vol 04 (11) ◽  
pp. 1563-1567 ◽  
Author(s):  
Franca Caliò ◽  
Elena Marchetti
Keyword(s):  
Singular Integral ◽  
Spline Approximation ◽  
Cubic Spline ◽  
Weakly Singular

scholarly journals A linear approximation for solutions of Abel–Volterra integral equations

2020 ◽  
Vol 14 (2) ◽  
pp. 596-604
Author(s):  
Mostefa Nadir
Keyword(s):  
Integral Equations ◽  
Linear Approximation ◽  
Singular Integral ◽  
Volterra Integral Equations ◽  
New Technique ◽  
Numerical Examples ◽  
Weakly Singular

Abstract In this work, we present a modified linear approximation for solving the first and the second kind Abel–Volterra integral equations. This approximation was used by the author to approximate a weakly singular integral on the curve. Noting that this new technique gives a good approximation of these solutions compared with several methods in several numerical examples.

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