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    Solutions to differential-differential difference equations with variable coefficients by using fourier transform method
    (2023) Düz, Murat; Avezov, Sunnet; Issa, Ahmad
    In this paper, differential-differential difference equations with variable coefficients have been solved using the Fourier Transform Method (FTM). In addition, new definitions and theorems are introduced. Besides, the efficiency of the proposed method is verified by solving five important examples. Furthermore, we have noted that the Fourier transform method is a powerful technique for solving ordinary differential difference equations (ODDEs) with variable coefficients. It involves transforming the ODDEs into the frequency domain using the Fourier transform, solving the transformed equation, and then applying the inverse Fourier transform to obtain the solution in the time domain.
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    Solving difference equations using fourier transform method
    (Yildiz Technical Univ, 2024) Avezov, Sunnet; Issa, Ahmad; Duz, Murat
    This article mainly focuses on presenting a new accurate technique (Fourier Transform Method) 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.