Non-Polynomial Collocation Spectral Scheme for Systems of Nonlinear Caputo-Hadamard Differential Equations
FRACTAL AND FRACTIONAL(2024)
Abstract
In this paper, we provide a collocation spectral scheme for systems of nonlinear Caputo-Hadamard differential equations. Since the Caputo-Hadamard operators contain logarithmic kernels, their solutions can not be well approximated using the usual spectral methods that are classical polynomial-based schemes. Hence, we construct a non-polynomial spectral collocation scheme, describe its effective implementation, and derive its convergence analysis in both L2 and L infinity. In addition, we provide numerical results to support our theoretical analysis.
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Key words
orthogonal functions,spectral methods,error analysis,Caputo-Hadamard derivative
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