Titlebook: Numerical Approximation of Ordinary Differential Problems; From Deterministic t Raffaele D‘Ambrosio Textbook 2023 The Editor(s) (if applica

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Discretization of the Problem,book: how to compute approximate solutions to initial values problems for ODEs. In this chapter we aim to introduce some basic concepts characterizing the discretization of ODEs, as well as basic accuracy and stability requirements that a numerical method has to fulfill. We realize that step-by-step

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Linear Multistep Methods,x methods could be useful in order to achieve better accuracy and stability properties. For this reason, we present a more general family of methods relying on a multistep structure and provide the analysis of accuracy and stability properties of linear multistep methods.

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Runge-Kutta Methods,abling better order and stability barriers. The strategy is novel with respect to that beyond linear multistep methods: indeed, it is no longer of multistep type, but we move to a multistage strategy relying on the information in some additional points, located inside each subinterval of the domain

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马笼头

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Stiff Problems,ccount. For instance, this is the case of the so-called stiff problems, usually occurring in mathematical modeling for several applications. This chapter is focused on the analysis of the main features of stiff problems and their numerical discretization. A typical phenomenon, consisting in the redu

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Geometric Numerical Integration, also to retaining qualitative properties of the continuous problem over long times. Sometimes such conservation properties naturally characterize the numerical schemes while, in more complex situations, preservation issues have to be conveyed into the numerical approximations. The numerical preserv

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Numerical Methods for Stochastic Differential Equations,erential equations, in order to both highlight basic accuracy and stability requirements and conservation issues along the numerical dynamics. A very brief introduction of Ito and Stratonovich calculus given, mostly in the direction of introducing the corresponding stochastic differential equations.

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rstand the clinical presentation of thyroid diseases, their defining histopathologic and cytopathologic features, and even the intricacies of patient management. Drs. Clark and Faquin have provided a valuable framework for cytologists learning (and continuing to learn) this exacting discipline. Org-