Uniform l(1) behaviour in a second-order difference-type method for a linear Volterra equation with completely monotonic kernel I: stability

作者：Xu, Da^*

来源：IMA Journal of Numerical Analysis, 2011, 31(3): 1154-1180.

DOI：10.1093/imanum/drq026

• Volterra equation
• completely monotonic kernel
• time discretization
• second-order backward differentiation formula method
• l(1) stability

where A is a self-adjoint densely defined linear operator on a Hilbert space H with a complete eigen-system {lambda(m), phi(m)}(m=1)(infinity) and beta(t) is completely monotonic and locally integrable, but not constant. The equation is discretized in time using second-order difference in combination with second order convolution quadrature for the memory term. The stability properties of the discretization in time are derived in the l(t)(1)(0,infinity; H) boolean AND l(t)(infinity) (0,infinity; H) norm.

• 出版日期2011-7
• 单位湖南师范大学