numerical solution of differential equations

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1: 3.7 Ordinary Differential Equations

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§3.7(ii) Taylor-Series Method: Initial-Value Problems

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§3.7(iii) Taylor-Series Method: Boundary-Value Problems

… ►The eigenvalues ${\lambda }_k$ are simple, that is, there is only one corresponding eigenfunction (apart from a normalization factor), and when ordered increasingly the eigenvalues satisfy … ►

§3.7(v) Runge–Kutta Method

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2: 16.25 Methods of Computation

… ►There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations). …

3: Ronald F. Boisvert

… ►His research interests include numerical solution of partial differential equations, mathematical software, and information services that support computational science. …

4: Bonita V. Saunders

… ►Her research interests include numerical grid generation, numerical solution of partial differential equations, and visualization of special functions. …

5: 2.7 Differential Equations

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§2.7(iv) Numerically Satisfactory Solutions

… ►In consequence, if a differential equation has more than one singularity in the extended plane, then usually more than two standard solutions need to be chosen in order to have numerically satisfactory representations everywhere. ►In oscillatory intervals, and again following Miller (1950), we call a pair of solutions numerically satisfactory if asymptotically they have the same amplitude and are $\frac{1}{2}\pi$ out of phase.

6: 18.38 Mathematical Applications

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Differential Equations: Spectral Methods

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Quadrature “Extended” to Pseudo-Spectral (DVR) Representations of Operators in One and Many Dimensions

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7: 36.15 Methods of Computation

… ►For numerical solution of partial differential equations satisfied by the canonical integrals see Connor et al. (1983).

8: 11.2 Definitions

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§11.2(iii) Numerically Satisfactory Solutions

… ►(11.2.17) applies when $|\mathrm{ph}z|\le \frac{1}{2}\pi$ with $z$ bounded away from the origin.

9: 9.2 Differential Equation

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§9.2(iii) Numerically Satisfactory Pairs of Solutions

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10: 12.2 Differential Equations

… ►All solutions are entire functions of $z$ and entire functions of $a$ or $\nu$. …