A Nyström interpolant for some weakly singular nonlinear Volterra integral equations
Copyright policy )A Nyström interpolant for some weakly singular nonlinear Volterra integral equations
The author considers the numerical solution of second kind Volterra integral equations with weakly singular kernel which is a non-compact operator, of the type \[ u(t)- \int^t_0 k(t,s)\Biggl({s\over t}\Biggr)^\mu {u(s)\over s} ds= f(t),\qquad t\in (0,T]> 0,\;\mu> 0, \] and \(f(t)\) a given function. A Nyström type interpolant of the solution based on Gauss-Radau nodes has been derived. The stability of interpolant is conformed by numerical tests and derived convergence estimates.
Computational Mathematics, Volterra integral equations, Applied Mathematics, weakly singular kernels, Weakly singular kernels, Numerical methods for integral equations
Computational Mathematics, Volterra integral equations, Applied Mathematics, weakly singular kernels, Weakly singular kernels, Numerical methods for integral equations
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