Differential equations continuity

Computational techniques are centrally important at every stage of investigation of nonlinear dynamical systems. We have reviewed the main theoretical and computational tools used in studying these problems among these are bifurcation and stability analysis, numerical techniques for the solution of ordinary differential equations and partial differential equations, continuation methods, coupled lattice and cellular automata methods for the simulation of spatiotemporal phenomena, geometric representations of phase space attractors, and the numerical analysis of experimental data through the reconstruction of phase portraits, including the calculation of correlation dimensions and Lyapunov exponents from the data. 

The physical aspects of any fluid flow are governed by three principles mass is conserved, Newton s second law is fulfilled (also referred as momentum equation) and energy is conserved these principles are expressed in integral equations or partial differential equations (continuity, momentum and energy equations), being the most common form the Navier-Stokes equations for viscous flows and the Euler equations for inviscid flows. 

Solution of the set of differential equations continues with the new value of y [calculated by Eq. (5.119)] until lAyl < e. 

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