Non-Polynomial Collocation Spectral Scheme for Systems of Nonlinear Caputo-Hadamard Differential Equations

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.