The time discretization in classes of integro-differential equations with completely monotonic kernels: weighted asymptotic stability
The paper is devoted to a study of the behaviour of a numerical method when used to discretize certain linear convolution type integro-differential equations whose kernels are linear combinations of finitely many completely monotonic functions with coefficients \(\geq 1\). The numerical scheme is a backward Euler method combined with a first-order convolution quadrature for the memory term. The main emphasis of the paper is on providing sufficient conditions for the numerical method to be asymptotically stable in a weighted norm on \((0, \infty)\).
weighted \(l ^{1}\) asymptotic stability
linear convolution type integro-differential equations
scientific article; zbMATH DE number 6151452
scientific article