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∞. In addition, we provide numerical results to support our theoretical analysis.

Keywords

• orthogonal functions
• spectral methods
• error analysis
• Caputo–Hadamard derivative