Solve math problems – numerical methods

Resources > Matlab > Solve math problems – numerical methods

Also see Resources > Matlab > Diffusion & Heat Transfer for more numerical method examples

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Topic

    MATLAB Examples
Simultaneous linear equations  

 

screen shot – for Workbook 7.4
m-file – for Workbook 7.4
Root of nonlinear equation M-file link.
As example, solve van der Waal’s equation for molar volume
using Newton’s method, fzero(), fminbnd(), interval halving
or bisection, successive approximation, the SYMBOLIC toolbox
and, since this happens to be a polynomial, roots().

Fit polynomial function to
data using “linear regression”

  • Notes 1 – fit polynomial to data
  • Notes 2 – fitting equations to data
  • a straight line is a graph of polynomial of order 1
 

 

Fit a polynomial to data using polyfit, polyval and linear algebra

 
Fitting nonlinear equation to data using “nonlinear regression” (“least squares fit”)

(yes, this example can be inverted and linearized but the methods work on nonlinear equations)

Problem statement

Problem solution with function lsqcurvefit. You must have the Optimization Toolbox installed in order to use lsqcurvefit.
> main file > function file

Problem solution with function fminsearch
> main file > function file
Differentiation and integration (quadrature) of data Integration of data
(quadrature)
Differentiation
of data – RTD tracer experiment
FreeMat users: search for Freemat note in file
Differentiation
of data from Batch Reactor

Integrate one Ordinary
Differential Equation (ODE)

 Integrating one ODE using
Euler’s method
Using Matlab’s ode45 function > main file > derivative function file

Integrate two coupled ODE’s

See notes in cell above

 Integrating two ODEs using
Euler’s method
Using Matlab’s ode45 function > main file > derivative function file

Integrate Partial Differential Equations (PDE) using the finite-difference method

  

Transient 1D diffusion – code, plots and notes

Transient 1D diffusion – code only