Abstract
Partial Fibonacci difference equation is introduced and subjected to investigation in discrete heat equation by having recourse to Fibonacci difference operator with shift values in this paper. By having Fourier law of cooling as its basis, the heat transfer in the long rod is investigated and the solutions obtained are validated by MATLAB.
Highlights
The difference operator defined on u(k) found its inception in 1984 by Jerzy Popenda [1, 4]
The study gained its momentum by the contribution of G.B.A.Xavier, et al,[3] when the k-difference operator with variable coefficients was k (l )
The need for a comprehensive operator arose as the investigation was carried out on heat equation and an extension of the operator termed as [5] was introduced with inputs gained from the other operators mentioned in the above literature
Summary
The difference operator defined on u(k) found its inception in 1984 by Jerzy Popenda [1, 4]. The study gained its momentum by the contribution of G.B.A.Xavier, et al,[3] when the k-difference operator with variable coefficients was k (l ). The need for a comprehensive operator arose as the investigation was carried out on heat equation and an extension of the operator termed as [5] was introduced. With inputs gained from the other operators mentioned in the above literature. 2. Fibonacci Difference Operator on Two Variable v(k) = u(k), = (0, 2) or ( 1,0); x = (x1, x2). We obtain the following heat equation model for a long rod. The operator in (1) becomes partial Fibonacci difference operator if either 1 or 2 is zero but not both. The equations involving a first order linear partial fibonacci difference equation [7] is
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