Titlebook: Applied Scientific Computing; With Python Peter R. Turner,Thomas Arildsen,Kathleen Kavanagh Textbook 2018 Springer International Publishing

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https://doi.org/10.1007/978-0-387-35503-0 and therefore to estimate them, or even mitigate them. Numerical processes are themselves finite. The finiteness of processes gives rise to truncation errors, for example resulting from restricting the number of terms in a series that we compute. In other settings it might be a spatial, or temporal

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https://doi.org/10.1007/978-0-387-35503-0mple, and often already familiar approaches like the trapezoid rule, including its relation to the fundamental concept of a Reimann sum. The trapezoid rule and Simpson’s rule are explored in more detail which then leads to a discussion of so-called composite integration rules where the interval of i

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Reiner Güttler,Ralf Denzer,Patrik Houyuce the two fundamental approaches: Jacobi and Gauss-Seidel iterations. Next we turn to (linear) least squares approximation. This refers to the problem of finding the “best” fit to specified data using a linear combination of simpler functions such as the terms of a polynomial. The final topic of t

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https://doi.org/10.1007/978-0-387-34951-0he polynomial) so that the interpolation can be local. The final topic for this chapter is spline interpolation. Here the basic idea is to use low degree polynomials which connect as smoothly as possible as we move through the data. The example we focus on is cubic spline interpolation where the res

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D. G. Peters,P. K. Robertson,R. L. Cordytwo can be used to advantage as a predictor-corrector pair. Treating the independent and dependent variables as vector quantities allows systems of differential equations to be approached using these same methods. Higher order differential equations can also be recast as systems of first-order equat

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