ordinary differential equations
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11—20 of 27 matching pages
11: 22.19 Physical Applications
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§22.19(iii) Nonlinear ODEs and PDEs
►Many nonlinear ordinary and partial differential equations have solutions that may be expressed in terms of Jacobian elliptic functions. …12: Bibliography B
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Ordinary differential equations.
Fourth edition, John Wiley & Sons, Inc., New York.
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The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods.
John Wiley & Sons Ltd., Chichester.
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Numerical Methods for Ordinary Differential Equations.
John Wiley & Sons Ltd., Chichester.
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13: 2.7 Differential Equations
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►An ordinary point of the differential equation
…All solutions are analytic at an ordinary point, and their Taylor-series expansions are found by equating coefficients.
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14: Bibliography W
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Asymptotic Expansions for Ordinary Differential Equations.
Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney.
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15: 18.38 Mathematical Applications
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►Linear ordinary differential equations can be solved directly in series of Chebyshev polynomials (or other OP’s) by a method originated by Clenshaw (1957).
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16: 1.13 Differential Equations
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►A standard form for second order ordinary differential equations with , and with a real parameter , and real valued functions and , with and positive, is
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17: Bibliography C
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Theory of ordinary differential equations.
McGraw-Hill Book Company, Inc., New York-Toronto-London.
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18: Bibliography M
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Hyperasymptotic solutions of second-order ordinary differential equations with a singularity of arbitrary integer rank.
Methods Appl. Anal. 4 (3), pp. 250–260.
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19: 3.11 Approximation Techniques
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►Also, in cases where satisfies a linear ordinary differential equation with polynomial coefficients, the expansion (3.11.11) can be substituted in the differential equation to yield a recurrence relation satisfied by the .
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