Abstract
Abstract Multi-term time-fractional partial differential equations (PDEs) have become a hot topic in the field of mathematical physics and are used to improve the modeling accuracy in the description of anomalous diffusion processes compared to the single-term PDE results. This research includes the numerical solutions of two-term time-fractional PDE models using an efficient and accurate local meshless method. Due to the advantages of the meshless nature and ease of applicability in higher dimensions, the demand for meshless techniques is increasing. This approach approximates the solution on a uniform or scattered set of nodes, resulting in well-conditioned and sparse coefficient matrices. Numerical tests are performed to demonstrate the efficacy and accuracy of the proposed local meshless technique.
Highlights
In the past decade, fractional partial differential equations (PDEs) have received a lot of attention
Rippa [53] recommended a technique known as leave-oneout cross-validation (LOOCV)-based algorithm to determine an appropriate shape parameter, which is modified by Fasshaeur and Zhang [54]
The MQ and inverse multiquadric (IMQ) radial basis function (RBF) are more stable in this case in comparison to inverse quadric (IQ) RBF, the conation number of IQ RBF is high than MQ and IMQ RBFs
Summary
Fractional partial differential equations (PDEs) have received a lot of attention. The RBF only depends on the Euclidean distance between two points in the spatial domain, so it increases the preferences and advantages of the meshless technique As indicated by these realities, the meshless method is a truly adaptable and helpful numerical technique and can be applied to enormous practical problems [44,45]. Rippa [53] recommended a technique known as leave-oneout cross-validation (LOOCV)-based algorithm to determine an appropriate shape parameter, which is modified by Fasshaeur and Zhang [54]. In light of the above discussed shortcomings such as sensitivity to the shape parameters value and ill-conditioned and dense system of algebraic equations, the researchers recommend the local meshless method (LMM) [58,59]. One irregular puncture domain is considered in numerical examinations
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