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Stability analysis and numerical implementation of the third-order fractional partial differential equation based on the Caputo fractional derivative

Rasheed Sarbast Kamal, Modanli Mahmut, Abdulazeez Sadeq Taha

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 3

33--42

This paper examines a third-order fractional partial differential equation (FPDE) in the Caputo sense. The Theta difference method (TDM) is utilized to investigate the problem, and a first-order difference scheme is developed. Stability estimates are obtained by applying the Von Neumann analysis method. A test problem is presented as an application, and numerical results are obtained using Matlab software. Error estimates, as well as exact and approximate solutions are presented in a data analysis table. The simulation results are shown through error analysis tables and figures.

Numerical scheme methods for solving nonlinear pseudo-hyperbolic partial differential equations

Abdulazeez Sadeq Taha, Modanli Mahmut, Husien Ahmad Muhamad

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 4

5--15

The numerical solutions to the nonlinear pseudo-hyperbolic partial differentia equation with nonlocal conditions are presented in this study. This equation is solved using the homotopy analysis technique (HAM) and the variational iteration method (VIM). Both strategies are compared and contrasted in terms of approximate and accurate solutions. The results show that the HAM technique is more appropriate, effective, and close to the exact solution than the VIM method. Finally, the graphical representations of the obtained results are given.