Stability of backward differentiation formulas for Volterra integro-differential equations
The paper deals with the system of Volterra integro-differential equations with linear convolution kernel \[ y'(t)= g(t)+ Ay(t)+ \int^t_0 k(t- s)y(s) ds,\quad t\in[0, T],\tag{1} \] \[ y(0)= y_0;\quad y, g\in\mathbb{R}^d;\quad A, k\in\mathbb{R}^{d\times d}.\tag{2} \] The author analyzes the numerical stability of backward differentiation methods for (1), (2).
system of Volterra integro-differential equations
scientific article; zbMATH DE number 1423344