An adaptive radial basis function approach for efficiently solving multidimensional spatiotemporal integrodifferential equations
This work addresses computational challenges in solving complex spatiotemporal equations for researchers in numerical analysis and applied mathematics, representing an incremental improvement with adaptive tuning.
The paper tackles the efficient solution of multidimensional spatiotemporal integrodifferential equations by proposing an adaptive radial basis function approach, which automatically adjusts RBF shapes to mitigate the curse of dimensionality and demonstrates effectiveness through numerical examples.
In this work, we propose an adaptive radial basis function (RBF) approach for the efficient solution of multidimensional spatiotemporal integrodifferential equations. Our approach can automatically adjust the shape of RBFs and provide an easy-to-implement and mesh-free approach for solving spatiotemporal equations. Specifically, we analyze how the proposed method mitigates the curse of dimensionality by adaptively adjusting the scales and centers of the radial basis functions when the solution is spatially anisotropic. Through a range of numerical examples, we demonstrate the effectiveness of our approach for solving multidimensional spatiotemporal integrodifferential equations.