To get familiar with ordinary differential equations in Matlab, methods for solving them, to perform basic results visualization and analysis.

Scientific & Engineering Programming

II Year Electronics and Computer Engineering, FoE, WUST

Laboratory Class 10 – ODEs in Matlab

The scope

To get familiar with ordinary differential equations in Matlab, methods for solving them, to perform basic results visualization and analysis.

Prerequisites

Before the classes you should know, how to:

• represent and define differential equations,

• solve numerically differential equations,

• visualize solution of the differential equation,

• model simple physical systems.

Tasks

1. Exercise the plots from the task 11, Lab Class 9, if not done earlier.

2. Solve the second order differential equation

y ⁰⁰ (x) + py ⁰ (x) + qy(x) = 0

for different values of p and q parameters. What is the influence of the sign of the character- istic equation discriminant (D = p ² − 4q) to the solution? Visualize the obtained results.

3. Solve the set of equations

( _dx

1

dt = x ₂

dx

dt = −x 1 − kx 2

.

Visualize and interpret the results for different initial conditions and values of the parameter k (large: k > 2 and small 0 < k < 2).

4. Solve the set of equations



 

 

dx

dt = −4x + 2y + 5z

dy

dt = 6x − y − 6z

dz

dt = −8x + 3y + 9z .

Visualize the results for different initial conditions.

5. Using the Newton’s laws write the differential equation of a harmonic oscillator of the mass m, which is a system that, when displaced from its equilibrium position, experiences a restoring force F , proportional to the displacement x:

F = −kx,

where k is a positive constant. Solve the equation and visualizing the obtained solution determine the motion characteristics.

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