Discretisation of abstract linear evolution equations of parabolic type

作者：Goncalves Fernando F^*; Grossinho Maria do Rosario; Morais Eva

来源：Advances in Difference Equations, 2012, 14.

DOI：10.1186/1687-1847-2012-14

• parabolic evolution equations
• finite-difference methods
• financial mathematics

We investigate the discretisation of the linear parabolic equation du/dt = A(t)u + f(t) in abstract spaces, making use of both the implicit and the explicit finite-difference schemes. The stability of the explicit scheme is obtained, and the schemes%26apos; rates of convergence are estimated. Additionally, we study the special cases where A and f are approximated by integral averages and also by weighted arithmetic averages. %26lt;br%26gt;MSC 2010: 65J10.

• 出版日期2012