Solving difference equations using fourier transform method

Yıl 2024, Cilt: 42 Sayı: 4, 1239 - 1244, 01.08.2024

Sunnet Avezov , Ahmad Issa , Murat Düz

Öz

This article mainly focuses on presenting a new accurate technique (Fourier Transform Meth-od) for solving linear of mth order Difference Equations with constant coefficients. Also, a new lower triangular matrix was introduced to overcome problems related to finding the Fourier Transform of polynomials by rewriting standard-based polynomials through the fallen power polynomial base. Besides, five examples have been presented to illustrate the validity and accuracy of this method. The results reveal that the Fourier transform method is very effective and attractive in solving the difference equations.

Anahtar Kelimeler

Coefficients Matrix, Fourier Transform Method, Non Homogeneous Linear Difference Equations

Kaynakça

• REFERENCES
• [1] Kelley W. G, Peterson A. C. Difference equations: an introduction with applications. Cambridge, Massachusetts: Academic Press; 2001.
• [2] Gupta R. C. On particular solutions of linear difference equations with constant coefficients. SIAM Rev 1998;40. [CrossRef]
• [3] Agarwal R. P. Difference equations and inequalities: theory, methods, and applications. Boca Raton, Florida: CRC Press; 2000. [CrossRef]
• [4] Avezov S, Düz M, Issa A. Solutions to differential-differential difference equations with variable coefficients by using fourier transform method. Süleyman Demirel Univ Fac Arts Sci J Sci 2023;18:259–267. [CrossRef]
• [5] Berinde V. A Method for Solving Second Order Difference Equations. In Cheng S, (editor). New Developments in Difference Equations and Application. London: Routledge; 2017. p. 4148. [CrossRef]
• [6] Feldmann L. On linear difference equations with constant coefficients. Period Polytech Electr Eng 1959;3:247–257.
• [7] Fort T. Linear difference equations and the Dirichlet series transform. Amer Math Monthly 1955;62:641–645. [CrossRef]
• [8] Olver F. W. Numerical solution of second-order linear difference equations. J Res Nat Bureau Stand 1967;71:111–129. [CrossRef]
• [9] Arikoglu A, Ozkol I. Solution of difference equations by using differential transform method. Appl Math Comput 2006;174:1216–1228. [CrossRef]
• [10] Hatipoglu V. F. Taylor polynomial solution of difference equation with constant coefficients via time scales calculus. New Trends Math Sci 2015;3:129.
• [11] Gencev M, Salounova D. First-and second-order linear difference equations with constant coefficients: suggestions for making the theory more accessible. Int J Math Educ Sci Technol 2022;54:1349–1372. [CrossRef]
• [12] Gupta RC. On linear difference equations with constant coefficients: An alternative to the method of undetermined coefficients. Math Mag 1994;67:131–135. [CrossRef]
• [13] Rivera-Figueroa A, Rivera-Rebolledo J. M. A new method to solve the second-order linear difference equations with constant coefficients. Int J Math Educ Sci Technol 2016;47:636–649. [CrossRef]
• [14] Rivera-Figueroa A, Rivera-Rebolledo JM. A response to Tisdell on ‘Critical perspectives of the “new” difference equation solution method’of Rivera-Figueroa and Rivera-Rebolledo. Int J Math Educ Sci Technol 2020;51:150–151. [CrossRef]
• [15] Tisdell C.C. Critical perspectives of the ‘new’difference equation solution method of Rivera-Figueroa and Rivera-Rebolledo. Int J Math Educ Sci Technol 2019;50:160–163. [CrossRef]
• [16] Düz M, Issa A, Avezov S. A new computational technique for Fourier transforms by using the differential transformation method. Bull Inter Math Virtual Inst 2022;12:287–295.