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Crank-Nicolson semi-implicit approach for numerical solutions of two- dimensional coupled nonlinear Burgers' equations

Srivastava V. K., Tamsir M.

International Journal of Applied Mechanics and Engineering

2012

Vol. 17, no. 2

571-581

The two-dimensional Burgers' equation is a mathematical model which is used to describe various kinds of phenomena such as turbulence and viscous fluid. In this paper, Crank-Nicolson semi-implicit scheme is used to handle such problem. The proposed scheme forms a system of linear algebraic difference equations to be solved at each time-step. The linear system is solved by direct method. Numerical results are compared with those of exact solutions and other available results. The present method performs well. To our best knowledge no one has solved Burgers' equations using this scheme. The proposed scheme can be extended for solving non-linear problems arising in various branches of engineering and science.

All-optical 4-bit parity checker design

Srivastava V. K., Priye V.

Optica Applicata

2011

Vol. 41, nr 1

157--164

A new configuration of all-optical 4-bit parity checker is proposed that incorporates six semiconductor optical amplifiers (SOAs). The proposed 4-bit parity generator is numerically simulated by solving nonlinear coupled equations that explain the cross gain modulation (XGM) effect in individual SOAs. The full design is easy to understand. The outputs can be tested at every step with the help of waveforms. This makes easy error analysis of the circuit. The fault detection and correction can be made comfortably. This design proves that when we reach up to chip level design, the economical circuit is integration capable.