Approximation methods for second kind weakly singular Volterra integral equations

Kant, Kapil; Nelakanti, Gnaneshwar

doi:10.1016/j.cam.2019.112531

Cited by 14 publications

(2 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where R α (x, t) is defined as (27). It is evident from Tables 7-11 that the PCCM and the PLCM provide high-precision accuracy rates as w increases.…”

Section: Numerical Examplesmentioning

confidence: 98%

“…Among numerical methods for VIEs, spectral methods have gained more interest from researchers. Some of the eminent methods are the differential transform method [22][23][24], Filon-type method [25], Levin's method [26], Galerkin and multi Galerkin methods [27], Chebyshev wavelet method [28], collocation method [29], Jacobi spectral collocation method [30,31], Chelyshkov collocation method [32,33], and the collocation boundary value method [34].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Collocation Numerical Method for Highly Oscillatory Algebraic Singular Volterra Integral Equations

SAIRA,

Ma,

Liu

2024

Fractal Fract

View full text Add to dashboard Cite

The highly oscillatory algebraic singular Volterra integral equations cannot be solved directly. A collocation numerical method is proposed to overcome the difficulty created by the highly oscillatory algebraic singular kernel. This paper is composed primarily of two methods—the piecewise constant collocation method and the piecewise linear collocation method—in which uniformly distributed nodes serve as collocation points. For the efficient computation of highly oscillatory and algebraic singular integrals, the steepest descent method as well as the Gauss–Laguerre and generalized Gauss–Laguerre quadrature rules are employed. Consequently, the resulting linear system is solved for the unknown function approximated by the Lagrange interpolation polynomial. Detailed theoretical analysis is carried out and numerical experiments showing high accuracy are also presented to confirm our analysis.

show abstract

“…where R α (x, t) is defined as (27). It is evident from Tables 7-11 that the PCCM and the PLCM provide high-precision accuracy rates as w increases.…”

Section: Numerical Examplesmentioning

confidence: 98%