Spectral collocation methods for Volterra-integro differential equations with noncompact kernels
The paper is devoted to a study of a numerical method for the linear Volterra integro-differential equation \(y'(t) + a(t) y(t) = \int_0^t s^{\mu-1}t^{-\mu} k(t,s) y(s) ds + g(t)\), \(t \in [0,T]\), subject to the initial condition \(y(0) = y_0\), with sufficiently smooth functions \(a\), \(g\) and \(k\) and \(\mu > 0\). The integral operator in this equation is not compact; this property makes the investigation more difficult. The authors begin by providing sufficient conditions for the existence and uniqueness of solutions and prove regularity properties of these solutions. Then, a spectral collocation method based on Chebyshev polynomials is developed and its convergence is analyzed.
linear Volterra integro-differential equation
scientific article; zbMATH DE number 6138051