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Spectral collocation method for Caputo fractional terminal value problems

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Abstract

Spectral collocation method is proposed to solve Caputo fractional terminal value problem. The main idea of the proposed method is to solve the corresponding nonlinear weakly singular Volterra-Fredholm integral equation. The key step in presented method is to transform the nonlinear integral kernels to linear integral kernels by a functional transformation. Then, the integral terms can be calculated exactly by Gauss quadrature formula. The provided convergence analysis shows that the presented method has spectral convergency. Theoretical results are confirmed by numerical experiments. The presented method makes some improvements to the existed methods.

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Funding

This work is supported by the Natural Science Foundation of Guangdong Province of China (2018A030313236) and the National Natural Science Foundation of China (11971123).

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Authors and Affiliations

  1. School of Financial Mathematics and Statistic, Guangdong University of Finance, Guangzhou, 510521, China

    Zhendong Gu

  2. School of Accounting, Guangdong University of Finance and Economics, Guangzhou, 510320, China

    Yinying Kong

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  1. Zhendong Gu
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  2. Yinying Kong
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Correspondence to Zhendong Gu.

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Gu, Z., Kong, Y. Spectral collocation method for Caputo fractional terminal value problems. Numer Algor 88, 93–111 (2021). https://doi.org/10.1007/s11075-020-01031-3

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  • DOI: https://doi.org/10.1007/s11075-020-01031-3

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