A New SDIMSIM Methods with Optimized Region of Stability and Sustainable Development with Applications On Neutrosophic Data - A.Y. J. Almasoodi; Mohammed Kadhim Mohsin; Sarah A.AL-Ameedee; Mohammed Amer Shanyoor (Neutrosophic Sets and Systems)
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.