Single Step Methods and Rational Approximations of Semigroups
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In this chapter we shall again study single step time stepping methods for a homogeneous parabolic equation in an abstract setting. This time we will use the semigroup approach and represent the time stepping operator as a Dunford-Taylor integral in the complex plane, which will allow us to treat more general elliptic operators than in the last chapter. For the purpose of including also application to maximum-norm estimates with respect to a spatial variable, which will be given at the end of the chapter, the analysis will take place in a Banach space framework.
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