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Solution of general inhomogeneous linear difference equations
Published online by Cambridge University Press: 17 February 2009
Abstract
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The general solution of the rth inhomogeneous linear difference equation is given in the form
The coefficients 
, i = 2, …, r, and b(n−r)(n) can be evaluated from n values 
, k = 0, …, n − 1, which santisfy an rth order homogenous linear difference equation. In the rth order homogeneous case and if n ≥ 2r, the method requires the evaluation of r determinants of successive orders n − 2r + 1, n − 2r + 2, …, n − r. If r ≤ n ≤ 2r − 1, only n − r determinants are required, with orders varying from 1 to n − r. In the second order ihnomogenous case, can be evaluated from a continued fraction amd a simple product.
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- Copyright © Australian Mathematical Society 1983
References
[1]Brown, A., “Solution of a linear difference equation”, Bull. Austral. Math. Soc. 11 (1974), 325–331.CrossRefGoogle Scholar
[2]Love, J. D., “Solution of homogeneous linear difference equations”, J. Austral. Math. Soc. Ser. B 21 (1980), 293–296.CrossRefGoogle Scholar
[3]Singh, V. N., “Solution of a general homogeneous linear difference equation”, J. Austral. Math. Soc. Ser. B 22 (1980), 53–57.CrossRefGoogle Scholar
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