The numerical solutions for a class of fifth-order partial differential equations via generalized RKM methods
*Murtadha A. KadhimCorresponding authormurtadha.abduljawad.iku@atu.edu.iqAffiliation 1Department of Applied MathematicsFaculty of Mathematical SciencesUniversity of MazandaranBabolsar, IranAffiliation 2Kufa Technical InstituteAl-Furat Al-Awsat Technical University (ATU)Najaf, IraqView full profile → , AllahBakhsh Yazdani Cheratiyazdani@umz.ac.irDepartment of Applied MathematicsFaculty of Mathematical SciencesUniversity of MazandaranBabolsar, IranView full profile → , Mohammed Sahib Mecheemohammeds.abed@uokufa.edu.iqInformation Technology Research and Development Center (ITRDC)University of KufaNajaf, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 17 Oct 2023
- Published Online:
- 31 May 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1762
- Pages:
- 729–735
Abstract
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References
[1] Mechee, M. S., & Kadhim, M. A. Explicit direct integrators of rk type for solving special fifth-order ordinary differential equations. American Journal of Applied Sciences, 13(12), 1452-1460 (2016).
[2] Holcapek, M., & Valášek, R. Numerical solution of partial differential equations with the help of fuzzy transform technique. In 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (pp. 1-6). IEEE (2017, July).
[3] Dlamini, P. G., & Khumalo, M. A new compact finite difference quasilinearization method for nonlinear evolution partial differential equations. Open Mathematics, 15(1), 1450-1462 (2017).
[4] Han, J., Jentzen, A., & E, W. Solving high-dimensional partial differential equations using deep learning. Proceedings of the National Academy of Sciences, 115(34), 8505-8510 (2018).
[5] Sun, H., Hou, M., Yang, Y., Zhang, T., Weng, F., & Han, F. Solving partial differential equation based on Bernstein neural network and extreme learning machine algorithm. Neural Processing Letters, 50, 1153-1172 (2019).
[6] Pourghanbar, S., Manafian, J., Ranjbar, M., Aliyeva, A., & Gasimov, Y. S. An efficient alternating direction explicit method for solving a nonlinear partial differential equation. Mathematical Problems in Engineering, 2020, 1-12 (2020).
[7] Ruthotto, L., & Haber, E. Deep neural networks motivated by partial differential equations. Journal of Mathematical Imaging and Vision, 62, 352-364 (2020).
[8] Li, W., & Pang, Y. Application of Adomian decomposition method to nonlinear systems. Advances in Difference Equations, 2020, 1-17 (2020).
[9] Wang, J., Cockayne, J., Chkrebtii, O., Sullivan, T. J., & Oates, C. J. Bayesian numerical methods for nonlinear partial differential equations. Statistics and Computing, 31, 1-20 (2021).
[10] Hairer, E., Norsett, S. P., and Wanner, G., Solving Ordinary Differential Equations I: Nonstiff Problems, Springer-Verlag, Berlin, Germany (1993).
[11] Sharma, S., & Obaid, A. J. Mathematical modelling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox. Journal of Interdisciplinary Mathematics, 23(4), 843-849 (2020).




