Asymptotic solutions to a discrete airy equation |
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Authors: | Ronald E Mickens |
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Institution: | Department of Physics , Clark Atlanta University , Atlanta, GA 30314, USA |
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Abstract: | A nonstandard finite difference scheme for the Airy equation leads to a linear, second—order difference equation for which the theorems of Poincaré and Perron do not apply if asymptotic representations of the solutions are desired. Using the method of dominant balance, a suggested form for the asymptotic solutions is obtained. This relation is then used to construct the required asymptotic representations for the two linearly independent solutions |
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Keywords: | Difference equations Asymptotic methods Airy equation Finite difference methods |
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