Table 1 Proposed method comparison with the previous methods.
From: Explicit scheme for solving variable-order time-fractional initial boundary value problems
Strategies | Methodology | Benefits and shortcomings |
|---|---|---|
Alia et al.41 proposed a new group of iterative techniques to address the numerical solution of a two-dimensional sub-diffusion equation that involves fractional derivatives and specific boundary conditions | These iterative schemes are designed to provide a robust and efficient means of solving two-dimensional sub-diffusion equations | This method is computationally efficient, but no stability analysis has been performed |
Oderinu et al.42 proposed a method that focuses on finding approximate solutions to linear time fractional differential equations under specific boundary conditions | It investigates a numerical approach for the solution of linear time fractional differential equations of the Caputo type. The results of the research culminated in the establishment of a theorem that showcases the Kamal transform of the nth-order Caputo derivatives | The proposed numerical scheme provides highly accurate solutions for linear time fractional differential equations. However, no stability analysis of the scheme has been performed. This method is limited in scope and can only be applied to linear time fractional differential equations |
Proposed | The proposed method uses the central finite difference method for approximating the second-order spatial derivative and forward difference for approximating the Caputo derivative of time. This combination of techniques allows for an efficient and accurate numerical approximation of the solutions to linear/semi-linear time fractional differential equations | This numerical scheme is versatile and can be applied to both linear and semi-linear equations, providing a flexible solution for a range of problems. The stability of the method has been rigorously verified, ensuring reliable results for a wide range of parameters. Additionally, the method is not limited by specific boundary conditions, making it suitable for a wide range of applications |
