Construction of Laguerre pseudospectral differentiation matrices

TL;DR

This paper introduces a stable, efficient method for constructing Laguerre pseudospectral differentiation matrices, improving numerical accuracy and robustness for large collocation point counts.

Contribution

It reformulates the matrix entries and employs a closed-form for diagonals, avoiding cancellation and enhancing stability over classical methods.

Findings

Improved numerical stability and accuracy demonstrated in experiments.

Method handles larger collocation point counts effectively.

Avoids catastrophic cancellation in matrix construction.

Abstract

In this paper, we present a stable and efficient approach for constructing Laguerre pseudospectral differentiation matrices. The proposed method reformulates the off-diagonal entries and computes all required quantities simultaneously using an existing fast algorithm that also generates the collocation nodes. For the diagonal entries, a closed-form expression is employed to improve numerical accuracy. This construction avoids the catastrophic cancellation present in classical formulations and yields an all-in-one procedure for generating differentiation matrices. Numerical experiments demonstrate improved robustness and sustained high accuracy for significantly larger numbers of collocation points compared to standard implementations.