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<p>In this paper, we show that reduction of order of homogeneous difference equations can be achieved through Lie symmetry method. Moreover, we solve a homogeneous difference equation of order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and investigate the dynamics of its solution. It turns out that its solution and that of its associated reduced equation can be expressed via generalized Fibonacci numbers.</p>

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HOMOGENEOUS DIFFERENCE EQUATIONS, LIE SYMMETRY AND FIBONACCI NUMBERS

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • M. Aloqeili

摘要

In this paper, we show that reduction of order of homogeneous difference equations can be achieved through Lie symmetry method. Moreover, we solve a homogeneous difference equation of order \(k+1\) k + 1 and investigate the dynamics of its solution. It turns out that its solution and that of its associated reduced equation can be expressed via generalized Fibonacci numbers.