Transcription of Discrete (Difierence) Equations - School of …
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Discrete (Difierence) Equations - School of …
Discrete (Difference) EquationsA Discrete , or difference, equation expresses a relationship between the elements of a sequence,{yn},wheren N0 {0,1,2, ..}. For example, the trivial difference equationyn+1=yn,(1)has the solutionyn=y0, which means that the sequence{yn}may be any constant mathematical models are posed in the form of Discrete Equations . The (in)famous logisticmapyn+1=ryn(1 yn),(2)was introduced as a model for the growth of a population. Here,yn [0,1] represents the (scaled)population in then-th year,y0is the initial population; andr >0 is a combined birth and Equations also arise when solving continuous models using numerical methods, a nec-essary task for all but the most simple models.
1 Linear difierence equations 1.1 Equations with constant coe–cients A general m-th order difierence equation with constant coe–cients can be written in the form amyn+m +am¡1yn+m¡1 +¢¢¢ +a1yn+1 +a0yn = rn; (4)
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