# M\"untz Pseudo Spectral Method: Theory and Numerical Experiments

## TL;DR

This paper introduces new non-classical Lagrange basis functions based on Jacobi-M"untz functions, develops associated interpolants, derives error bounds, and demonstrates their effectiveness through numerical experiments.

## Contribution

The paper proposes novel non-classical Lagrange basis functions derived from Jacobi-M"untz functions, along with new interpolants and error analysis, advancing spectral methods.

## Key findings

- New basis functions improve spectral approximation accuracy
- Derived error bounds validate the interpolants' effectiveness
- Numerical experiments confirm computational efficiency

## Abstract

This paper presents two new non-classical Lagrange basis functions which are based on the new Jacobi-M\"untz functions presented by the authors recently. These basis functions are, in fact, generalizations form of the newly generated Jacobi based functions. With respect to these non-classical Lagrange basis functions, two non-classical interpolants are introduced and their error bounds are proved in detail. The pseudo-spectral differentiation (and integration) matrices have been extracted in two different manners. Some numerical experiments are provided to show the efficiency and capability of these newly generated non-classical Lagrange basis functions.