numerical differentiation
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1—10 of 12 matching pages
1: 3.4 Differentiation
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§3.4(i) Equally-Spaced Nodes
… ► ►§3.4(ii) Analytic Functions
… ►§3.4(iii) Partial Derivatives
… ►2: 3.3 Interpolation
3: Philip J. Davis
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►Davis also co-authored a second Chapter, “Numerical Interpolation, Differentiation, and Integration” with Ivan Polonsky.
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4: 18.40 Methods of Computation
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►See Gautschi (1983) for examples of numerically stable and unstable use of the above recursion relations, and how one can then usefully differentiate between numerical results of low and high precision, as produced thereby.
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5: Bibliography M
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6: 10.45 Functions of Imaginary Order
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►In consequence of (10.45.5)–(10.45.7), and comprise a numerically satisfactory pair of solutions of (10.45.1) when is large, and either and , or and , comprise a numerically satisfactory pair when is small, depending whether or .
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7: 10.24 Functions of Imaginary Order
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►In consequence of (10.24.6), when is large and comprise a numerically satisfactory pair of solutions of (10.24.1); compare §2.7(iv).
Also, in consequence of (10.24.7)–(10.24.9), when is small either and or and comprise a numerically satisfactory pair depending whether or .
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8: 3.7 Ordinary Differential Equations
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§3.7(ii) Taylor-Series Method: Initial-Value Problems
… ►By repeated differentiation of (3.7.1) all derivatives of can be expressed in terms of and as follows. … ► … ►§3.7(v) Runge–Kutta Method
… ►The method consists of a set of rules each of which is equivalent to a truncated Taylor-series expansion, but the rules avoid the need for analytic differentiations of the differential equation. …9: 20.14 Methods of Computation
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►Similarly, their -differentiated forms provide a convenient way of calculating the corresponding derivatives.
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►In practice a value with, say, , , is found quickly and is satisfactory for numerical evaluation.