numerical solution
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11: 11.2 Definitions
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§11.2(iii) Numerically Satisfactory Solutions
… ►When , , and , numerically satisfactory general solutions of (11.2.7) are given by … ►When and , numerically satisfactory general solutions of (11.2.7) are given by … ►When , numerically satisfactory general solutions of (11.2.9) are given by …(11.2.17) applies when with bounded away from the origin.12: 10.25 Definitions
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§10.25(iii) Numerically Satisfactory Pairs of Solutions
►Table 10.25.1 lists numerically satisfactory pairs of solutions (§2.7(iv)) of (10.25.1). … ►13: 2.7 Differential Equations
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§2.7(iv) Numerically Satisfactory Solutions
… ►This kind of cancellation cannot take place with and , and for this reason, and following Miller (1950), we call and a numerically satisfactory pair of 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 out of phase.14: Bibliography K
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The second Painlevé equation in electric probe theory. Some numerical solutions.
Zh. Vychisl. Mat. Mat. Fiz. 38 (6), pp. 992–1000 (Russian).
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The second Painlevé equation in the electrostatic probe theory: Numerical solutions for the partial absorption of charged particles by the surface.
Technical Physics 49 (1), pp. 1–7.
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15: Bibliography P
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Numerical Solution of Sturm-Liouville Problems.
Monographs on Numerical Analysis, The Clarendon Press, Oxford University Press, New York.
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16: 9.2 Differential Equation
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§9.2(iii) Numerically Satisfactory Pairs of Solutions
►Table 9.2.1 lists numerically satisfactory pairs of solutions of (9.2.1) for the stated intervals or regions; compare §2.7(iv). ► …17: 10.2 Definitions
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§10.2(iii) Numerically Satisfactory Pairs of Solutions
►Table 10.2.1 lists numerically satisfactory pairs of solutions (§2.7(iv)) of (10.2.1) for the stated intervals or regions in the case . … ►18: 18.40 Methods of Computation
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►Usually, however, other methods are more efficient, especially the numerical solution of difference equations (§3.6) and the application of uniform asymptotic expansions (when available) for OP’s of large degree.
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19: 14.2 Differential Equations
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