## Numerical solution to a simple ode

August 04, 2011 at 12:44 AM | categories: odes | View Comments

# Numerical solution to a simple ode:

Integrate this ordinary differential equation (ode)

## Contents

over the time span of 0 to 2. The initial condition is y(0) = 1.

to solve this equation, you need to create a function or function handle of the form: dydt = f(t,y) and then use one of the odesolvers, e.g. ode45.

```
function main
```

## problem setup

y0 = 1; % initial condition y(t=t0) t0 = 0; tend=2; tspan = [t0 tend]; % span from t=0 to t=2 [t,y] = ode45(@myode,tspan,y0); % here is where you get the solution plot(t,y) xlabel('time') ylabel('y(t)')

## analytical solution

Hopefully you recognize the solution to this equation is . Let's plot that on the same graph. We will use a dashed red line

hold on plot(t,exp(t),'r--') legend('numerical solution','analytical solution') % these are clearly the same solution.

```
'end'
```

ans = end

```
function dydt = myode(t,y)
```

differential equation to solve

dydt = y; % categories: ODEs % tags: math