Multistep Backward Difference Methods
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In this chapter we shall first consider approximations at equidistant time levels of parabolic equations in which the time derivate is replaced by a multistep backward difference quotient of maximum order consistent with the number of time steps involved. We show that when this order is at most 6, then the method is stable and has a smoothing property analogous to that of single step methods of type IV. We shall use these properties to derive both smooth and nonsmooth data error estimates. In the end of the chapter we shall also discuss the use of two-step backward difference operators with variable time steps.
KeywordsDifference Method Multistep Method Eigenfunction Expansion Variable Time Step Constant Time Step
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