Different Computational Approach for Sumudu Integral Transform by Using Differential Transform Method

Year 2018, , 233 - 238, 20.12.2018

Murat Gübeş

https://doi.org/10.32323/ujma.433172

Abstract

In this work, we present a different technique for calculation of Sumudu Integral Transform (SIT) by considering differential transform method (DTM). By means of our technique, Sumudu Transform of functions is obtained easily without complicated integration procedures.

Keywords

Sumudu transform, Differential transform method, Numerical solutions, Computational method

References

• [1] G. K. Watugala, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Internat. J. Math. Ed. Sci. Tech., 24(1) (1993), 35–43.
• [2] F. B. M. Belgacem, A. A. Karaballi, S. L. Kalla, Analytical investigations of the Sumudu transform and applications to integral production equations, Math. Probl. Eng., 3 (2003), 103–118.
• [3] F. B. M. Belgacem, Sumudu transform applications to Bessel functions and equations, Appl. Math. Sci., 4 (2010), 3665–3686.
• [4] G. K. Watugala, Sumudu transform new integral transform to solve differential equations and control engineering problems, Math. Engrg. Ind., 6(4) (1998), 319–329.
• [5] A. Kilicman, H. E. Gadain, An Application of Double Laplace transform and double Sumudu transform, Lobachevskii J. Math., 30(3) (2009), 214–223.
• [6] A. Kilicman, H. E. Gadain, On the applications of Laplace and Sumudu transforms, J. Franklin Inst., 347(5) (2010), 848–862.
• [7] M. Zahid, M. A. Rana, T. Haroon, A. Siddiqui, Applications of Sumudu transform to MHD flows of an Oldroyd-B fluid, Appl. Math. Sci., 7 (2013), 7027–7036.
• [8] M. A. Rana, A. Siddiqui, Q. K. Ghori, R. Qamar, Application of He’s Homotopy perturbation method to Sumudu transform, Int. J. Nonlinear Sci. Numer. Simul., 8(2) (2007), 185–190.
• [9] N. A. A. Rahman, M. Z. Ahmad, Applications of the fuzzy Sumudu transform for the solution of first order Fuzzy differential equations, Entropy, 17(7) (2015), 4582–4601.
• [10] O. M. Ogunlaran, H. S. Yusuf, Adomain Sumudu transform method for the Blasius equation, British J. Math. Comput. Sci., 14(3) (2016), 1–8.
• [11] S. Abbasbandy, Applications of He’s homotopy perturbation method for Laplace transform, Chaos Solitons Fractals, 30(5) (2006), 1206–1212.
• [12] H. Fatoorehchi, H. Abolghasemi, N. Magesh, The differential transform method as a new computational tool for Laplace transforms, Nats. Akad. Sci. Lett., 38(2) (2015), 157–160.
• [13] E. Babolian, J. Biazar, A. R. Vahidi, A new computational method for Laplace transforms by decomposition method, Appl. Math. Comput., 150(3) (2004), 841–846.
• [14] C. K. Chen, S. H. Ho, Solving partial differential equations by two-dimensional differential transform method, Appl. Math. Comput., 106(2-3) (1999), 171–179.
• [15] M. J. Jang, C. Li Chen and Y. C. Liy, On solving the initial-value problems using the differential transformation method, Appl. Math. Comput., 115(2-3) (2000), 145–160.
• [16] M. Gubes, H. A. Peker, G. Oturanc, Application of Differential transform method for El Nino southern oscillation (ENSO) model with compared Adomian decomposition and variational iteration methods, J. Math. Comput. Sci., 15(3) (2015), 167–178.
• [17] M. Gubes, G. Oturanc, Approximate solutions of coupled Ramani equation by using RDTM with compared DTM and exact solutions, New Trends Math. Sci., 4 (2016), 198-212.