Comparison of the Accuracy of an Improved MPS Numerical Method and a Meshless Method Based on Taylor Expansion and Least Squares

Author

Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran

10.22034/ceej.2025.64486.2397

Abstract

The Moving Particle Semi-implicit (MPS) is one of the efficient meshless numerical methods that has been successfully used to analyze various engineering problems. In this method, the approximation of the derivatives of the function is performed based on a weighted averaging by interpolation functions. Despite its inherent capabilities, this method has serious shortcomings, especially in terms of accuracy. Many efforts have been made to improve the accuracy of this method. In this study, the accuracy of one of the most efficient MPS models (Model 1 in this study) is compared with a meshless method based on the least squares technique and Taylor expansion (Model 2 in this study) for solving elliptic differential equations. Numerical results show that numerical Model 2 produces much better results and under these conditions, it can be expected that this numerical model can be successfully used to solve many engineering problems.

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References

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Journal of Civil and Environmental Engineering
Volume 55, Issue 121 - Serial Number 121
Winter 2026
January 2026
Pages 27-38

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