Review of Methods for Nonlinear Algebraic Equations

This appendix presents a number of solution methods to solve systems of algebraic equations. We will start with the basic techniques, such as bisection and successive substitution, and then discuss one of the most widely used Newton-Raphson methods. These methods are useful in solving roots of 

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APPENDIX A Review of Methods for Nonlinear Algebraic Equations... 

APPENDIX A Review of Methods for Nonlinear Algebraic Equations Solving for a from Eq. A. 19, we obtain... 

Sargent, R. W. H., A Review of Methods for Solving Nonlinear Algebraic Equation, Foundations of Computed Aided Chemical Process Design, Engineering Foundation, New York, Vol. 1, 1980, pp. 27-76. 

Diffusion and mass transfer in multicomponent systems are described by systems of differential equations. These equations are more easily manipulated using matrix notation and concepts from linear algebra. We have chosen to include three appendices that provide the necessary background in matrix theory in order to provide the reader a convenient source of reference material. Appendix A covers linear algebra and matrix computations. Appendix B describes methods for solving systems of differential equations and Appendix C briefly reviews numerical methods for solving systems of linear and nonlinear equations. Other books cover these fields in far more depth than what follows. We have found the book by Amundson (1966) to be particularly useful as it is written with chemical engineering applications in mind. Other books we have consulted are cited at various points in the text. 

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