Extraction of Some New Solutions of Linear Differential Equations by Dual Space

Year 2020, , 176 - 183, 31.12.2020

Gülay Koru Yücekaya

https://doi.org/10.47000/tjmcs.808617

Abstract

In this study, the solutions of second order linear homogeneous ordinary differential equations being variable and constant coefficients have been obtained by using power series method which is used frequently in dual space. The solutions of second order homogeneous ordinary differential equations being constant and variable coefficients in dual space by using power series have given and some applications have implemented.

Keywords

Dual number, Dual function, Analytic function, Linear differential equation, Power series

References

• Asil, V., Aydın, M.E., Küçükarslan, Z., Çınar, G., Tatlıpınar, S., The solution of differential equations using dual functions, e-Journal of NWSA, 4(4)(2009), Article number: 3A0012.
• Aydın, M., Kuryel, B., Gündüz, G., Oturanç, G., Differential Equations and Applications, E.U. Textbooks Publications of Faculty of Engineering, No.14, İzmir, 2001.
• Hacısalihoğlu, H.H., General dual motion of n moving reference frames}, Communications de la Faculte des Sciences De l'Universite d'Ankara, (1971), 71--85.
• Hacısalihoğlu, H.H., Motion Geometry and Quaternions Theory, Gazi University Faculty of Arts and Science Publications, Math. 2, 1983.
• Jimenez, N.G, Torba, S.M., Spectral parameter power series representation for solutions of linear system of two first order differential equations, Applied Mathematics and Computation, 370(124911), (2020), 1--10.
• Mak, M., Koru Yücekaya, G., Çetinkaya, A., On the solutions of differential equations with series of powers in dual space, VII. National Geometry Symposium, 07-10 July 2009, Kırşehir, Turkey, (2009).
• Ritger, Paul D., Rose, Nicholas J., Differential Equations with Applications, NY, Dover Publications, IX., 2000.
• Ross, Shepley L., Differential Equations, John Wiley and Sons, Inc., 1974.
• Veldkamp, G.R., em On the use dual numbers, vectors and matrices in instantaneous spatial kinematics, Mech. Mach Theory, 11(1976), 141--156.
• Yang, A.T., Application of Quaternion Algebra and Dual Numbers to Analysis of Spatial Mechanisms, Doctoral Dissertation, Columbia University, 1963.
• Yaşar, İ.B., Differential Equations and Applications, Siyasal Bookstore, 2nd. Ed., Ankara, 1999.