PDE Models and Riemann-Stieltjes Integrals in Sustainability

TL;DR

This paper introduces new PDE-based models combined with Riemann-Stieltjes integrals to measure sustainability, providing a practical formula for sustainability indices applicable to real-world multi-dimensional data.

Contribution

It develops novel PDE models integrated with Riemann-Stieltjes integrals for assessing sustainability, suitable for complex multi-variate data and real-world applications.

Findings

Proposed a new global sustainability model using PDEs and Riemann-Stieltjes integrals.

Developed a practical formula for sustainability indices with key variables.

Demonstrated the model with a civil engineering case study.

Abstract

Understanding sustainability through modeling involves one of the complex and interdisciplinary activities where mathematics plays a key role. We provide arguments favoring the need for developing global models for measuring the status of sustainability. A global model (applicable in broader perspective) and global sustainability indices are proposed which can be used with real-world data. The solutions of the proposed Partial Differential Equations (PDEs) are blended with the weight functions of Riemann Stieltjes integrals to capture the differential importance of sustainability associated factors. The ideas, methods, and models are new and are prepared for handling multi-dimensional and multi-variate data. A practically adaptable formula for measuring the sustainability index is developed with few key variables. We provide a real-world example arising in civil engineering applications with a numerical example to demonstrate our models.