ODE solvers (ode45) in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is ode45 used for in MATLAB?

ode45 is a MATLAB function used to solve ordinary differential equations (ODEs) numerically. It is based on a Runge-Kutta method and is good for solving non-stiff ODEs.

beginner

What type of problems is ode45 best suited for?

ode45 works best for solving non-stiff ordinary differential equations where the solution changes smoothly.

beginner

How do you define the function to be solved by ode45?

You define a function that returns the derivative (rate of change) of your variable(s). It usually looks like dy = f(t,y), where t is time and y is the current value.

beginner

What is the basic syntax to call ode45?

The basic syntax is [t,y] = ode45(@odefun, tspan, y0); where @odefun is your function, tspan is the time interval, and y0 is the initial condition.

beginner

What do the outputs t and y from ode45 represent?

t is a column vector of time points where the solution is evaluated. y is a matrix where each row corresponds to the solution at the time in t.

Which MATLAB function is commonly used for solving non-stiff ODEs?

A ode45

B ode15s

C ode23s

D ode113

ode45 is designed for non-stiff ODEs, while ode15s and ode23s are for stiff problems.

What does the function passed to ode45 return?

A The time span

B The derivative of the state variables

C The initial conditions

D The solution vector

The function returns the derivatives (rates of change) of the variables at a given time and state.

In the call [t,y] = ode45(@odefun, [0 10], 5);, what does 5 represent?

A Step size

B Final time

C Initial value of the variable

D Derivative value

The number 5 is the initial condition for the variable at time 0.

What is the output y from ode45?

A Time points vector

B Initial conditions

C Derivative function handle

D Solution values at each time point

y contains the solution values corresponding to each time in t.

If your ODE problem is stiff, which solver is better than ode45?

A ode15s

B ode23

C ode45

D ode23t

ode15s is designed for stiff problems and is more efficient than ode45 in those cases.

Explain how to use ode45 to solve a simple ODE in MATLAB.

Think about the steps from writing the function to getting the solution vectors.

Describe the difference between stiff and non-stiff ODEs and which MATLAB solvers are suitable for each.

Consider how the solution behavior affects solver efficiency.