Airy equation
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1: 9.16 Physical Applications
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►A quite different application is made in the study of the diffraction of sound pulses by a circular cylinder (Friedlander (1958)).
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►Again, the quest for asymptotic approximations that are uniformly valid solutions to this equation in the neighborhoods of critical points leads (after choosing solvable equations with similar asymptotic properties) to Airy functions.
…An application of Airy functions to the solution of this equation is given in Gramtcheff (1981).
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►Reference to many of these applications as well as to the theory of elasticity and to the heat equation are given in Vallée and Soares (2010): a book devoted specifically to the Airy and Scorer functions and their applications in physics.
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►Solutions of the Schrödinger equation involving the Airy functions are given for other potentials in Vallée and Soares (2010).
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2: 9.2 Differential Equation
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Table 9.2.1: Numerically satisfactory pairs of solutions of Airy’s equation.
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§9.2(i) Airy’s Equation
… ►§9.2(ii) Initial Values
… ►§9.2(iii) Numerically Satisfactory Pairs of Solutions
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§9.2(vi) Riccati Form of Differential Equation
…3: 9.13 Generalized Airy Functions
§9.13 Generalized Airy Functions
►§9.13(i) Generalizations from the Differential Equation
… ► … ►Each of the functions and satisfies the differential equation …and the difference equation …4: 9.11 Products
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§9.11(i) Differential Equation
…5: Bibliography S
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An algorithm for the evaluation of the complex Airy functions.
J. Comput. Phys. 31 (1), pp. 60–75.
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A Riccati approach to the Airy equation.
In Asymptotic and computational analysis (Winnipeg, MB, 1989), R. Wong (Ed.),
pp. 403–415.
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An extension of Airy’s equation.
SIAM J. Appl. Math. 15 (6), pp. 1400–1412.
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6: 9.10 Integrals
7: 36.10 Differential Equations
8: 9.18 Tables
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