Leonhard Euler (Image source)
This program will allow you to obtain the numerical solution to the first order initial value problem (IVP):
| dy/dt = f(t,y) on [t0, t1] | ||
| y(t0) = y0 |
Three different methods are provided to solve the problem: Euler's method, Heun's method (also known as the improved Euler method), and a fourth-order Runge-Kutta method. To solve a problem, choose a method, fill in the fields below, choose the output format, and then click on the "Submit" button.
Mathematical expressions are entered just as they would be in most programming languages:
- use * for multiply,
- use / for divide, and
- use ^ to raise a quantity to a power.
A wide range of functions (e.g. exp(t) and sinh(t)) are supported. Whitespace is allowed.
For example, the function (1+y2) sin(et) would be entered as (1+y^2)*sin(exp(t)).