Abstract
In this paper, the authors develop a direct method used to solve the initial value problems of a linear non-homogeneous time-invariant difference equation. In this method, the obtained general term of the solution sequence has an explicit formula, which includes coefficients, initial values, and right-side terms of the solved equation only. Furthermore, the authors find that when the solution sequence has a nonzero first term, it satisfies two adjoint linear recursive equations; this usually shows several new features of the solution sequence.
Highlights
We give mainly attention to the convolution (Cauchy multiplication) of two sequences
If the sequence c is a convolution of two sequences a and b, expressed as a ∗ b = b ∗ a = c, the general term c(k) of the sequence c is [ ]
In the second section of this paper, based on these relationships between sequences and their BS-matrices as mentioned above, we develop a direct method used to solve the initial value problem of a linear, time-invariant, non-homogeneous difference equation
Summary
We give mainly attention to the convolution (Cauchy multiplication) of two sequences. In the second section of this paper, based on these relationships between sequences and their BS-matrices as mentioned above, we develop a direct method used to solve the initial value problem of a linear, time-invariant, non-homogeneous difference equation. The general term of solution sequence has an explicit formula, which includes coefficients and initial values of the solved equation only.
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