Differential transform method for the solutions to some initial value problems in chemistry

1. Z. Xu, Numerical simulation of the coalescence of two bubbles in an ultrasound field. Ultrason. Sonochem. 49, 277–282 (2018)

   Article  CAS  Google Scholar 

2. K. Yasui, T. Tuziuti, J. Lee, T. Kozuka, A. Towata, Y. Iida, The range of ambient radius for an active bubble in sonoluminescence and sonochemical reactions. J. Chem. Phys. 128, 184705 (2008)

   Article  Google Scholar 

3. X. Tong, T.E. Simos, A complete in phase FinitDiff procedure for DiffEquns in chemistry. J. Math. Chem. 58, 407–438 (2020)

   Article  CAS  Google Scholar 

4. M.M. Khalsaraei, A. Shokri, M. Molayi, The new class of multistep multiderivative hybrid methods for the numerical solution of chemical stiff systems of first order IVPs. J. Math. Chem. 58, 1987–2012 (2020)

   Article  CAS  Google Scholar 

5. P. Roul, A new mixed MADM-Collocation approach for solving a class of Lane-Emden singular boundary value problems. J. Math. Chem. 57, 945–969 (2019)

   Article  CAS  Google Scholar 

6. H. Madduri, P. Roul, A fast-converging iterative scheme for solving a system of Lane-Emden equations arising in catalytic diffusion reactions. J. Math. Chem. 57, 570–582 (2019)

   Article  CAS  Google Scholar 

7. Y.P. Qin, Z. Wang, L. Zou, Dynamics of nonlinear transversely vibrating beams: Parametric and closed-form solutions. Appl. Math. Modell. 88, 676–687 (2020)

   Article  Google Scholar 

8. Y.P. Qin, Q.J. Lou, Z. Wang, L. Zou, Kudryashov and Sinelshchikov’s method for solving the radial oscillation problem of multielectron bubbles in liquid helium. J. Math. Chem. 58, 1481–1488 (2020)

   Article  CAS  Google Scholar 

9. Y.P. Qin, Analytical solution for the collapse motion of an empty hyper-spherical bubble in \(N\) dimensions. Phys. Lett. A 384, 126142 (2020)

   Article  CAS  Google Scholar 

10. Y.P. Qin, Z. Wang, L. Zou, M.F. He, Parametric analytical solution for the \(N\)-dimensional Rayleigh equation. Appl. Math. Lett. 76, 8–13 (2018)

    Article  Google Scholar 

11. G. Scholz, F. Scholz, First-order differential equations in chemistry. ChemTexts 1, 1 (2014)

    Article  Google Scholar 

12. J.H. He, F.Y. Ji, Taylor series solution for Lane-Emden equation. J. Math. Chem. 57, 1932–1934 (2019)

    Article  CAS  Google Scholar 

13. Z. Odibat, An optimized decomposition method for nonlinear ordinary and partial differential equations. Phys. A 541, 123323 (2020)

    Article  Google Scholar 

14. Z. Wang, Y.P. Qin, L. Zou, Analytical solutions of the Rayleigh-Plesset equation for \(N\)-dimensional spherical bubbles. Sci. China Phys. Mech. Astron. 60, 104721 (2017)

    Article  Google Scholar 

15. J.K. Zhou, Differential Transformation and Its Application for Electrical Circutits (Huazhong University Press, Wuhan, 1986). (in Chinese)

    Google Scholar 

16. Y.P. Qin, Z. Wang, L. Zou, M.F. He, Semi-numerical, semi-analytical approximations of the Rayleigh equation for gas-filled hyper-spherical bubble. Int. J. Comput. Meth. 16, 1850094 (2019)

    Article  Google Scholar 

17. Y.W. Lin, K.H. Chang, C.K. Chen, Hybrid differential transform method/smoothed particle hydrodynamics and DT/finite difference method for transient heat conduction problems. Int. Commun. Heat. Mass Trans. 113, 104495 (2020)

    Article  Google Scholar 

18. S. Owyed, M.A. Abdou, A.H. Abdel-Aty, W. Alharbi, R. Nekhilie, Numerical and approximate solutions for coupled time fractional nonlinear evolutions equations via reduced differential transform method. Chaos Soliton Fract. 131, 109474 (2020)

    Article  Google Scholar 

19. L. Zou, Z. Wang, Z. Zong, Generalized differential transform method to differential-difference equation. Phys. Lett. A 373, 4142 (2009)

    Article  CAS  Google Scholar 

20. A. Tari, S. Shahmorad, Differential transform method for the system of two-dimensional nonlinear Volterra integro-differential equations. Comput. Math. Appl. 61, 2621–2629 (2011)

    Article  Google Scholar 

Download references