Comparison of two different implementations of a finite-difference-method for first-order pde in mathematica and matlab

TL;DR

This paper compares two implementations of a symmetric finite difference method for solving a first-order PDE related to crack length distribution in brittle materials, highlighting differences in computational approaches.

Contribution

It introduces and compares two different software implementations of a finite difference algorithm for a specific PDE modeling crack evolution.

Findings

Both implementations accurately model crack length distribution.

Differences in computational efficiency and accuracy are analyzed.

The study provides insights into implementation choices for similar PDE problems.

Abstract

In this article two implementations of a symmetric finite difference algorithm for a first-order partial differential equation are discussed. The considered partial differential equation discribes the time evolution of the crack length distribution of microcracks in brittle materia.