Differential Equations

This chapter presents two functions for solving ordinary differential equations (ODEs).

Ordinary Differential Equations

numEclipse implements two methods for solving ODE, i.e., ode45 and ode78. These open source functions are adopted from GNU Octave.

[T,Y] = ode45(func,ts,x0)

[T,Y] = ode78(func,ts,x0)

Both of these functions solve initial value problems for ODEs. ode45 uses 4^rth and 5^th order Runga-Kutta methods, whereas ode78 uses order 7 and 8 methods.

Here is an example of how to use ode45 function.

#func.m

# This function evaluates the population of competing species.

function y = func(t, x)
u = x(1);
v = x(2);
y = zeros(2, 1);
y(1) = 3 * u - (5/2) * u * v;
y(2) = 2 * v -  u * v;
 

> ts = [0 2.5];

> x0 = [0.2 0.18];

> [t, y] = ode45(@func, ts, x0);

> plot(t, y(:, 1))

Following plot shows the population evolution for specie 1.

> plot(t, y(:, 2))

Following plot shows the population evolution for specie 2.