Abstract
While attempting to approximate differential equations using Kansa’s radial basis function (RBF) collocation, we need to solve a non-symmetric, highly ill-conditioned system. There are many attempts to evaluate RBF interpolant in a more stable manner using approaches like Laurent series expansion, regularization, QR algorithms, etc. In this article, we modify the regularization method and obtain regularization parameter that reduces the ill-conditioning and provide stable solutions for fractional differential equations using Kansa’s asymmetric collocation. Numerical results are provided to illustrate the algorithm.
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Prashanthi, K.S., Chandhini, G. (2019). Regularization of Highly Ill-Conditioned RBF Asymmetric Collocation Systems in Fractional Models. In: Singh, V., Gao, D., Fischer, A. (eds) Advances in Mathematical Methods and High Performance Computing. Advances in Mechanics and Mathematics, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-030-02487-1_5
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