Four strategies for solving the

non-linear equation system which arises from the LHI discretization of the generic non-linear convection diffusion reaction equation (1) are tested.

Such restrictions yield a reduction in the convergence time of the numerical method compared to previous models [4][5] that do not provide a bounded search range or starting points for the solutions of the

non-linear equation systems.

Complex assembly analysis and advanced

non-linear equation solving, combined with large-tolerance joint handling capabilities, are some of the features of GGCM that DCS leveraged.

Since the equilibrium constants are a priori known, a system of

non-linear equations may be obtained.

However, having determined steady complex moduli, one can avoid the time integration of the significantly

non-linear equations of the model describing inelastic behaviour of the material.

The analytical solutions of the governing

non-linear equations are obtained using inverse methods.

Newton Raphson Method [15] is the most popular method for finding the roots of

non-linear equations.

Using the exact analysis in the final balance is complicated because it leads to

non-linear equations that have no usable analytical solutions.

The mathematical models of steady-state reactive distillation involve the solution of a system of

non-linear equations.

Using the point matching method a system of

non-linear equations is formed in a way to satisfy boundary conditions for the system.

Beginning with a primer on numEclipse, an open source mathematics programming language similar to the proprietary MATLAB, the volume provides information on solving

non-linear equations, designing solving systems for linear equations, computational eigenvalue problems, finite difference schemes, and interpolation and approximation.

Finding the roots of a single variable

non-linear equations efficiently, is a very interesting and old problem in numerical analysis and has many applications in engineering and other applied sciences.