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SIMULATIONS

Nonlinear Equations

 

Bisection Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Slow convergence of bisection method simulation [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Newton-Raphson Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Division by zero [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Slow Convergence at Inflection Points [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Root jumps over several roots [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Roots oscillates around local maxima and minima [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Secant Method

   

Simulation of secant method  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence Simulation of secant method  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Division by zero in secant method simulation  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Pitfall: Root jumps over several roots in secant method  [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

     

SIMULTANEOUS LINEAR EQUATIONS

 

Gaussian Elimination

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Gauss-Seidel Method

   

Method [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

   

Convergence [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

 

LU Decomposition

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

     

Interpolation

 

Direct Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Newton's Divided Difference Method

   

Method [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

 

Lagrange Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Spline Method

   

Method [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

     

REGRESSION

 

Linear Regression

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Nonlinear Regression

   

Without Data Linearization [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

With Data Linearization [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

Polynomial Regression [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

Comparing with and without Data Linearization [MAPLE]  [MATHCAD]  [MATHEMATICA]  [MATLAB]

 

Adequacy of a Regression Model

   

Adequacy [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

     

Integration

 

Trapezoidal Rule

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Simpson's 1/3rd Rule

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Romberg Rule

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Gauss-Quadrature Rule

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Integrating Discrete Functions

   

Integrating discrete functions [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

ORDINARY DIFFERENTIAL EQUATIONS

 

Euler's Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Runge-Kutta 2nd order Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Runge-Kutta 4th order Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Convergence [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Shooting Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

 

Finite Difference Method

   

Method [MAPLE] [MATHCAD] [MATHEMATICA] [MATLAB]

Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468 and 0717624.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.