A quantitative metric for robustness of nonlinear algebraic equation solvers

2011 ◽  
Vol 81 (12) ◽  
pp. 2673-2687 ◽  
Author(s):  
M. Sielemann ◽  
G. Schmitz
Keyword(s):  
Algebraic Equation ◽  
Nonlinear Algebraic Equation

scholarly journals A Nonlinear System Related to Investment under Uncertainty Solved using the Fractional Pseudo-Newton Method

2020 ◽  
Vol 63 (1) ◽  
pp. 41-53
Author(s):  
A. Torres-Hernandez ◽  
◽  
F. Brambila-Paz ◽  
J. J. Brambila ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Nonlinear System ◽  
Fractional Calculus ◽  
Algebraic Equation ◽  
Fractional Derivatives ◽  
Equation System ◽  
Nonlinear Algebraic Equation ◽  
Investment Under Uncertainty ◽  
Several Variables ◽  
Derivatives Of

A nonlinear algebraic equation system of two variables is numerically solved, which is derived from a nonlinear algebraic equation system of four variables, that corresponds to a mathematical model related to investment under conditions of uncertainty. The theory of investment under uncertainty scenarios proposes a model to determine when a producer must expand or close, depending on his income. The system mentioned above is solved using a fractional iterative method, valid for one and several variables, that uses the properties of fractional calculus, in particular the fact that the fractional derivatives of constants are not always zero, to find solutions of nonlinear systems.

scholarly journals A Collocation Method for Solving Fractional Riccati Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yalçın Öztürk ◽  
Ayşe Anapalı ◽  
Mustafa Gülsu ◽  
Mehmet Sezer
Keyword(s):  
Differential Equation ◽  
Collocation Method ◽  
Algebraic Equation ◽  
Nonlinear Algebraic Equation ◽  
Riccati Differential Equation ◽  
Solution Function ◽  
Delay Term ◽  
Collocation Points ◽  
Taylor Expansions ◽  
Equation With Delay

We have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.

A Comparison of the Performance of Nonlinear Equation Solvers for Machine Design Problems

1994 ◽  
Vol 116 (4) ◽  
pp. 1169-1171
Author(s):  
R. Agrawal ◽  
N. Sridhar ◽  
G. L. Kinzel
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Equation ◽  
Algebraic Equation ◽  
Nonlinear Equations ◽  
Machine Design ◽  
Nonlinear Algebraic Equation ◽  
Test Cases ◽  
Design Problems ◽  
Design Variables ◽  
Purpose Of Evaluation

Often, the mathematical modeling of mechanical components leads to a set of nonlinear equations which have to be solved in order to compute the design variables. This paper discusses the performance of six different nonlinear, algebraic-equation solvers useful for machine design problems. Problems from spring design are taken as test cases for the purpose of evaluation.

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