A finite difference/spectral scheme is proposed for the time fractional Ito equation. The mass conservation and stability of the numerical solution are deduced by the energy method in the L2 norm form. To reduce the computation costs, the fast Fourier transform technic is applied to a pair of equivalent coupled differential equations. The effectiveness of the proposed algorithm is verified by the first numerical example. The mass conservation property and stability statement are confirmed by two other numerical examples.
Dakang Cen, Zhibo Wang, Seakweng Vong
. Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic[J]. Communications on Applied Mathematics and Computation, 2023
, 5(4)
: 1591
-1600
.
DOI: 10.1007/s42967-022-00223-z
1. Canuto, C., Hussaini, M., Quarteroni, A., Zang, T.: Spectral methods in fluid dynamics. Springer-Verlag, New York (1988)
2. Cao, W., Xu, Y., Zheng, Z.: Finite difference/collocation method for a generalized time-fractional KDV equation. Appl. Sci. 8, 42 (2018)
3. Cen, D., Wang, Z.: Time two-grid technique combined with temporal second order difference method for two-dimensional semilinear fractional sub-diffusion equations. Appl. Math. Lett. 129, 107919 (2022)
4. Cen, D., Wang, Z., Mo, Y.: Second order difference schemes for time-fractional KdV-Burgers’ equation with initial singularity. Appl. Math. Lett. 112, 106829 (2021)
5. Gupta, A., Ray, S.: Numerical treatment for the solution of fractional fifth-order Sawada-Kotera equation using second kind Chebyshev wavelet method. Appl. Math. Model. 39, 5121-5130 (2015)
6. Heydari, M., Avazzadeh, Z., Atangana, A.: Shifted Vieta-Fibonacci polynomials for the fractal-fractional fifth-order KdV equation. Math. Method. Appl. Sci. 44, 6716-6730 (2021)
7. Ito, M.: An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher orders. J. Phys. Soc. Jpn. 49, 771-778 (1980)
8. Iyiola, O.: A numerical study of Ito equation and Sawada-Kotera equation both of time-fractional type. Adv. Math. Sci. J. 2, 71-79 (2013)
9. Li, L., Li, D.: Exact solutions and numerical study of time fractional Burgers equations. Appl. Math. Lett. 100, 106011 (2020)
10. Luo, D., Huang, W., Qiu, J.: A hybrid LDG-HWENO scheme for KdV-type equations. J. Comput. Phys. 313, 754-774 (2016)
11. Poochinapan, K., Wongsaijai, B.: A novel convenient finite difference method for shallow water waves derived by fifth-order Kortweg and De-Vries-type equation. Numer. Methods Partial Differential Equations (2022). https://doi.org/10.1002/num.22875
12. Sun, Z., Ji, C., Du, R.: A new analytical technique of the L-type difference schemes for time fractional mixed sub-diffusion and diffusion-wave equations. Appl. Math. Lett. 102, 106115 (2020)
13. Wang, J., Xu, T., Wang, G.: Numerical algorithm for time-fractional Sawada-Kotera equation and Ito equation with Bernstein polynomials. Appl. Math. Comput. 338, 1-11 (2018)
14. Wazwaz, A.: The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations. Appl. Math. Comput. 184, 1002-1014 (2007)
15. Ye, X., Cheng, X.: The Fourier spectral method for the Cahn-Hilliard equation. Appl. Math. Comput. 171, 345-357 (2005)
