MATLAB-Based Meshless Method for Solving Partial Differential Equations Using Radial Basis Functions
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Resource Overview
This repository provides MATLAB source code implementing a meshless method with radial basis functions (RBFs) for solving partial differential equations (PDEs), featuring numerical analysis techniques and implementation details.
Detailed Documentation
This MATLAB code implements a meshless method using radial basis functions (RBFs) to solve partial differential equations. The meshless approach eliminates the need for traditional grid generation, making it particularly suitable for complex geometries and high-dimensional spaces. The implementation incorporates numerical analysis and approximation techniques, including elements from finite element and finite difference methods. Key algorithmic components involve RBF interpolation for field approximation and collocation methods for discretizing PDE operators. The code includes detailed documentation explaining the methodology and usage instructions to help users better understand and utilize this approach. Implementation features automatic node generation, RBF kernel selection (such as Gaussian or multiquadric functions), and sparse matrix handling for efficient computation.
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