Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Runge-Kutta theory for Volterra and Abel integral equations of the second kind

“…Consequently, in a step-by-step fashion we may reduce the problem to the case r = 0, which is already known from (13). (The reduction from r = 1 to r -0 has actually been performed above.)…”

“…The special case a = -? (Abel equation in the proper sense) often arises in physical problems (see the references in [13] or [7]). Positive values of a are encountered in various biological models [2] and in statistics [14].…”

Linear Multistep Methods for Volterra Integral and Integro-Differential Equations

“…Moreover, this experiment indicates that the MML methods are to be considered as promising methods for weakly singular equations of the type given here, and that it would be interesting to compare them with other methods for this type of integral equations (see, e.g., [19]). …”

“…Example 2.4.3 (Weakly singular equations). Finally we show that VLM methods may be used for integrating weakly singular equations, a standard example of which is given by [19] y(t) = l + 2ft-('y-^, 0<,<4,…”

Complex B-spline Collocation method for solving weakly singular Volterra integral equations of the second kind

“…During the past few decades, this equation has been used to study various problems of mathematical chemistry and physics, such as reactions including stereology, heat conduction with mixed boundary conditions [10], crystal growth, electrochemistry, c 2015 Miskolc University Press super fluidity and the radiation of heat [7], electrochemistry, semi-conductors, scattering theory, seismology, heat conduction, metallurgy, fluid flow, chemical reactions and population dynamics [12,13,27], the particle transport problems of astrophysics, potential theory and Dirichlet problem, electrostatic and radiative heat transfer problems and in some engineering fields [29,30], astronomy, optics, computational electromagnetic, quantum mechanics, seismology image processing [1,6].…”