Difference schemes for solving the Cauchy problem for a second-order operator differential equation

作者：Kokurin M M^*

来源：Computational Mathematics and Mathematical Physics, 2014, 54(4): 582-597.

DOI：10.1134/S0965542514040083

• ill-posed problem
• operator differential equation
• Banach space
• Cauchy problem
• difference scheme
• convergence rate
• error estimate
• regularizing algorithm
• operator calculus

A class of finite-difference schemes for solving an ill-posed Cauchy problem for a second-order linear differential equation with a sectorial operator in a Banach space is studied. Time-uniform estimates of the convergence rate and the error of such schemes are obtained. Previously known estimates are improved due to an optimal choice of initial data for a difference scheme.

• 出版日期2014-4