摘要
We study discretization in classes of integro-differential equations where the functions aj(t),1≤j≤n,are completely monotonic on(0,∞) and locally integrable,but not constant.The equations are discretized using the backward Euler method in combination with order one convolution quadrature for the memory term.The stability properties of the discretization are derived in the weighted l1(ρ;0,∞) norm,where ρ is a given weight function.Applications to the weighted l1 stability of the numerical solutions of a related equation in Hilbert space are given.
We study discretization in classes of integro-differential equationswhere the functions aj（t）, 1 ≤ j ≤n, are completely monotonic on （0, ∞） and locally integrable, but not constant. The equations are discretized using the backward Euler method in combination with order one convolution quadrature for the memory term. The stability properties of the discretization are derived in the weighted 11 （p; 0, ∞） norm, where p is a given weight function. Applications to the weighted l^1 stability of the numerical solutions of a related equation in Hilbert space are given.
基金
supported by National Natural Science Foundation of China(Grant No.10971062)
关键词
积分微分方程
时间离散化
稳定性能
加权
单调
Hilbert空间
EULER方法
内核
the classes of integro-differential equation, completely monotonic kernel, backward Euler method,convolution quadrature, weighted l^1 asymptotic stability
