Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Advancement in technology and engineering poses us with many challenges, similarly in order to overcome such engineering challenges with the help of numerous mathematical models, equations are taken. Since in the beginning Mathematicians, Designers and Engineers strive for correctness and accuracy while solving equations Differential equations, in particular, hold a tremendous application in engineering and many other domains. One such type of Differential equation is known as partial differential equation. The spectrum of application of partial differential equations consists of simulation, algorithm generation, and analyzation of higher order PDE and wave equations. Adapting different numerical methods leads to a variety of answers and difference among them, therefore the selection of the method of solving is one of the crucial parameters to generate precise results. Our work focuses on the review of different numerical methods in order to solve Linear and Nonlinear differential equations on the basis of accuracy and efficiency, so as to reduce the iterations. These would be harmonizing guidelines to existing numerical methods of linear and nonlinear partial differential equations. © IJSTR 2020.

Department of Mathematics

School of Advanced Sciences

Vellore Campus

World University root node

International Journal of Scientific and Technology Research

Solving linear and non-linear partial differential equations using numerical techniques

We obtain an expression for the total northward mass transport in a porous bed of large extant subject to a stress applied at the top free surface using  -plane approximation. It is found that  -effect is found to be responsible for western intensification of ocean currents. The total northward transport of fluid (See Sverdrup [11]) is found to be closed through the western boundary layer (See: Stommel [4]) in the presence of porous medium.

VIT Unitversity

International Journal of Innovative Technology and Exploring Engineering Regular Issue

Northward Transport in a Stress Driven Flow Confined to a Porous Medium (Sverdrup Relation in a Porous Medium)

Stability of solutions plays an important role in the qualitative theory of difference equations. This is evident from a large number of research papers dedicated to it [1]. However, stability results for nabla fractional difference equations are scant. In this paper, we investigate the same for a class of linear nabla fractional difference equations involving Riemaim - Liouville and Caputo type fractional differences.

Proceedings of the Jangjeon Mathematical Society

Stability of linear nabla fractional difference equations

Difference equations are often used to analyze sampled data systems, in which stability problems are considered to be important. This is evident from a large number of research papers dedicated to it. However, stability results for nonlinear nabla fractional difference equations are not yet reported. The present article discusses stability of nonlinear nabla fractional difference equations of Riemann-Liouville and Caputo type, using fixed point theory. © 2014, Forum-Editrice Universitaria Udinese SRL. All rights reserved.