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Regularization of Highly Ill-Conditioned RBF Asymmetric Collocation Systems in Fractional Models

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Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 41)

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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.National Institute of Technology KarnatakaSurathkalIndia

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