A New SDIMSIM Methods with Optimized Region of Stability and Sustainable Development with Applications On Neutrosophic Data

Abstract

: General Linear Methods (GLMs) were introduced as logical extensions of the conventional Runge–Kutta 
and linear multistep methods. In the scenario when second derivatives, in addition to first derivatives, can be 
computed, a GLM modification known as SGLMs (GLM with second derivative) was created. The development of 
SDIMSIMs for the second type is presented in this study. For SDIMSIMs construction, we give examples with 
parameters (p, q, r, s), namely p = q = r = s = 1..., 4, where r is the number of external stages, s is the number of internal 
stages, p is the order, and q is the stage order. Furthermore, we will prove that those approaches are the largest area 
contained by the A-Stability and L-Stability properties; in addition to their mathematical importance, SDIMSIMs 
contribute widely to sustainable development by unlocking complex systems in climate modeling, renewable 
energy, ecological monitoring, epidemiological studies, etc. SDIMSIMs address this challenge by enhancing the 
numerical performance of these simulations and thus contributing to decreased resource consumption, lower 
energy demand and better computational sustainability. In this paper, we conduct construction and stability 
certificate for SDIMSIMs, and the supporting capacity of SDIMSIM for supporting sustainable solutions to global 
issues is certified.Also, we apply our study on some neutrosophic data with indeterminacy element (I), and compare the results. 

DOI: 10.5281/zenodo.15009437