Legendre spectral collocation methods for pantograph Volterra delay-integro-differential equations
A Legendre spectral collocation method is proposed for linear pantograph Volterra delay integro-differential equations. The method is based on a basis of Lagrange interpolation polynomials of order \(N\) using Legendre-Gauss points as knots and on the Gauss quadrature formula. The main contribution of this paper is the convergence analysis providing that the errors of the approximate solution and approximate first order derivative decay exponentially in \(L^2\)-norm and \(L_\infty\)-norm. Two numerical examples on the interval \([-1,1]\) and \([0,20]\), respectively, are presented in order to illustrate the effectiveness and the performances of the method showing the exponential decay of the errors plotted for \(1<N<17\) both for the approximate solution and for its first derivative.
Volterra delay integro-differential equations
linear pantograph Volterra delay integro-differential equations
scientific article; zbMATH DE number 6134430
scientific article