ABS methods for nonlinear systems of algebraic equations

Chapter 4 Systems of nonlinear algebraic equations

As with the scalar case, the equation is satisfied only at selected values of x = r = [r1, r2, · · · , rn], called the roots. The separation process model discussed in section §1.3.1 (variations 2 and 3, in particular) and the reaction sequence model of section §1.3.5 are two of the many examples in chemical engineering that give rise to such non-linear system of equations. As with the scalar c...

Comparing Solvers for Large Systems of Nonlinear Algebraic Equations

The solution of systems of nonlinear algebraic equations is a problem which complexity grows as the number of equations increases. The number of engineering problems, which led to these systems, is increasing each year. In this paper we compare the performance of four advanced solvers for systems of nonlinear algebraic equations which have been collected from Internet repositories. We are parti...

Waveform Relaxation Methods of Nonlinear Integral - Differential - Algebraic Equations

WAVEFORM RELAXATION METHODS OF NONLINEAR INTEGRAL-DIFFERENTIAL-ALGEBRAIC EQUATIONS ∗1) Yao-lin Jiang (Department of Mathematical Sciences, Xi’an Jiaotong University, Xi’an 710049, China) Abstract In this paper we consider continuous-time and discrete-time waveform relaxation methods for general nonlinear integral-differential-algebraic equations. For the continuous-time case we derive the conve...

Sign Methods for Enumerating Solutions of Nonlinear Algebraic Systems

We implement the concept of topological degree to isolate and compute all zeros of systems of nonlinear algebraic equations when the only computable information required is the algebraic signs of the components of the function. The basic theorems of Kronecker–Picard theory relate the number of roots to the topological degree. They are combined with grid methods in order to compute the topologic...

J un 2 00 1 NUMERICAL PERFORMANCE OF ABS CODES FOR NONLINEAR SYSTEMS OF EQUATIONS 1