Product integration methods based on discrete spline quasi-interpolants and application to weakly singular integral equations

Abstract

International audienceQuadrature formulae are established for product integration rules based on discrete spline quasi-interpolants on a bounded interval. The integrand considered may have algebraic or logarithmic singularities. These formulae are then applied to the numerical solution of integral equations with weakly singular kernels

Discrete biquintic spline method for Fredholm integral equations of the second kind

“…The use of splines in the numerical solution of integral equations has been investigated by many authors [2], [4], [10], [12], [13], [15], [16], [21], [26], [29]. While most of these work employs continuous splines, there are only very few papers that involve discrete splines, as such our work naturally complements the literature and in particular is applicable to more general integral equations.…”

Solutions of Fredholm integral equations via discrete biquintic splines

“…The use of splines in the numerical solution of integral equations has been investigated by many authors [7][8][9][10][22][23][24][25][26][27][28][29]. While most of these studies employ continuous splines, there are only very few papers that involve discrete splines, as such our work naturally complements the literature and in particular is applicable to more general integral equations.…”

On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials

“…Table 4 shows the absolute errors which computed by using proposed method. Also, Comparison is made with the result presented in [10,18]. There the maximum error is de ned as MaxError = max|ϕ(x) − ϕ N (x)|, to calculate the errors in Table 4.…”