THERMAL SCIENCE
International Scientific Journal
NUMERICAL SIMULATION OF 3-D SOBOLEV EQUATION VIA LOCAL MESHLESS METHOD
ABSTRACT
In this study, we use an effective meshless method to estimate the numerical solution of 3-D time-fractional Sobolev equation. The recommended meshless method is used for the spatial derivatives while the Liouville-Caputo derivative technique is utilized for the time derivative portion of the model equation. Accuracy of the method is assessed via error norms and comparison is made with the exact solution and other numerical methods given in more current literature, which demonstrated that the suggested strategy produces excellent performance and is more computationally efficient.
KEYWORDS
PAPER SUBMITTED: 2022-08-20
PAPER REVISED: 2022-09-28
PAPER ACCEPTED: 2022-11-15
PUBLISHED ONLINE: 2023-01-21
- Diethelm, K., The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Springer Science and Business Media, Berlin, Germany, 2010
- Caputo, M., Linear Models of Dissipation Whose Q is almost Frequency Independent-II, Geophysical Journal International, 13 (1967) 5, pp. 529-539
- Wang, F., et al., Gaussian Radial Basis Functions Method for Linear and Non-Linear Convection-Diffusion Models in Physical Phenomena, Open Physics, 19 (2021), 1, pp. 69-76
- Wang, F., et al., Formation of Intermetallic Phases in Ion Implantation, Journal of Mathematics, 2020 (2020), ID8875976
- Nawaz, R., et al., An Extension of Optimal Auxiliary Function Method to Fractional Order High Dimensional Equations, Alexandria Engineering Journal, 60 (2021), 5, pp. 4809-4818
- Ahmad, I., et al., Application of Local Meshless Method for the Solution of Two Term Time Fractional-Order Multi-Dimensional PDE Arising in Heat and Mass Transfer, Thermal Science, 24 (2020), Suppl. 1, pp. 95-105
- Ahmad, I., et al., Numerical Simulation of PDE by Local Meshless Differential Quadrature Collocation Method, Symmetry, 11 (2019) 3, 394
- Ahmad, I., et al., An Efficient Local Formulation for Time-Dependent PDE, Mathematics, 7 (2019), 216
- Ahmad, I., et al., Local RBF Method for Multi-Dimensional Partial Differential Equations, Computers and Mathematics with Applications, 74 (2017), 2, pp. 292-324
- Shu, C., Differential Quadrature and Its Application in Engineering, Springer-Verlag, London, UK, 2000
- Haq, S., Hussain, M., Application of Meshfree Spectral Method for the Solution of Multi-Dimensional Time-Fractional Sobolev Equations, Engineering Analysis with Boundary Elements, 106 (2019), Sept., pp. 201-216
- Ulutas, E., et al., Bright, Dark, and Singular Optical Soliton Solutions for Perturbed Gerdjikov-Ivanov Equation, Thermal Science, 25 (2021), Special Issue 2, pp. S151-S156
- Ulutas, E., et al., Exact Solutions of Stochastic KdV Equation with Conformable Derivatives in white Noise Environment, Thermal Science, 25 (2021), Special Issue 2, pp. S143-S149
- Yildirim, E. N., et al., Reproducing Kernel Functions and Homogenizing Transforms, Thermal Science, 25 (2021), Special Issue 2, pp. S9-S18
- Abdelrahman, M. A. E., et al., Exact Solutions of the Cubic Boussinesq and the Coupled Higgs Systems, Thermal Science, 24 (2020), Suppl. 1, pp. S333-S342
- Menni, Y., et al., Heat and Mass Transfer of Oils in Baffled and Finned Ducts, Thermal Science, 24 (2021), Suppl. 1, pp. S267-S276
