Showing papers by "Vivek Kumar published in 2022"

A comparative study of high‐resolution methods for nonlinear hyperbolic problems

Abstract: This paper reviews some of the established high‐resolution (HR) schemes for computing solutions to hyperbolic systems by means of a finite volume (FV) framework. The objective of this research is to assess the ability of various HR flux limiting techniques to capture intense shocks and discontinuities. A crucial design factor in developing these methods is selecting a suitable flux‐limiter, so a review of different flux‐limiters for standard explicit FV frameworks has also been included. A brief discussion of the HR total variation diminishing (TVD) numerical schemes, starting from some historical introduction, going on to exploring the design principles behind the HR, second‐order, oscillation free schemes, turning towards high order nonlinear techniques and ending with an overview of some of the most significant developments and applications in the last decades has been covered. Several one‐dimensional and two‐dimensional benchmark examples with severe and challenging wave configurations have been utilized to compare the various numerical approaches. These nonlinear test cases have been selected such that the computational setups are as basic as possible.

A prey–predator model approach to increase the production of crops: Mathematical modeling and qualitative analysis

Abstract: This paper expresses the concepts, methods, and applications of mathematical models in agriculture. We propose and analyze an ecosystem consisting of two types of preys and their predators; here the prey-I like sugarcane crops that take a long time to grow and prey-II like vegetables, which have a short life, are grown with sugarcane crops and predators that harm both prey-I and prey-II. The various equilibria of the system are obtained, and the stability conditions are analyzed. Furthermore, a comprehensive analysis of the optimal control strategy is also performed. The optimal control model includes the use of three control variables, such as pesticide application rate, biomass application rate, and control of Cassava mosaic virus in the system. Finally, we apply Pontryagin’s maximum principle to find the optimal control. Furthermore, analytical results are verified by numerical simulations.

Enhanced pairing‐free identity‐based broadcast authentication protocol in WSN using ElGamal ECC

Abstract: Authentication among the various communicating devices within wireless sensor networks during broadcasting is most significant among the other primary security services. This authentication during broadcasting services allows multiple mobile end‐devices to transmit messages dynamically and securely for fasten consumer tracking and sustaining privacy of the data transferred in the insecure sensor network. To enhance this authentication protocol for secure end‐users message distribution, this research work has introduced a novel identity (ID) based cryptographic technique that employs ElGmal‐elliptic‐curve cryptography and digital signature without implementing bilinear paring operation to reduce huge burden of computation overhead. Additionally, to accelerate the performance of the proposed authentication protocol, the size of the signature along with the encryption key is minimized. Eventually, the authentication protocol provides comparatively less computational complexity with secure and faster key management. The performance analysis supports the aforesaid claim as well as reflects the supremacy of the proposed scheme over the handover authentication protocol and bilinear pairings based authentication schemes.