How to Use MATLAB for Mathematical Modelling

You are still turning a real problem into a mathematical description and then using computation to explore it.

Check Your Model Before Trusting the Results

This is probably the most important part of the whole process.

A MATLAB script running without an error does not prove that your model is correct.

Before accepting the results, check:

Units

Make sure your quantities use compatible units.

Mixing seconds with minutes or metres with millimetres can produce results that look perfectly legitimate while being completely wrong.

Initial Conditions

For dynamic models, confirm that the starting values represent the actual situation.

Boundary Conditions

For physical models, make sure the conditions at the boundaries make sense.

Assumptions

Ask yourself whether the simplifications you made are reasonable.

Numerical Method

Check that the solver is appropriate for the mathematical problem.

Validation

Compare your results with measured data, an analytical solution, a published benchmark, or another trusted calculation whenever possible.

This last step is particularly important because modelling is an approximation of reality. The purpose is not to create a perfect copy of the real world. The purpose is to create a useful representation whose limitations you understand.

Keep Your MATLAB Model Organised

A complicated model can become difficult to maintain surprisingly quickly.

I recommend keeping parameters together near the beginning of the script and putting repeated calculations into functions.

For example:

% Model parameters
mass = 2;
springConstant = 50;
damping = 1.5;

% Simulation settings
tspan = [0 10];

% Run model