| Title | Summary |
|---|---|
| Euler's Method | Paul's On-Line Notes on the Euler method. This presentation of numerical methods is not as complete as ours. It does not cover the Runge-trapeziodal, Runge-midpoint, or Runge-Kutta methods. It does not cover the order of a method. |
| Euler's Numerical Method for y'=f(x,y) | Professor Mattuck (MIT video) discusses the explicit Euler method,
the Runge-trapezoidal method, and the (standard) Runge-Kutta method for constructing numerical solutions of y'=f(x,y). He mentions four common names for the Runge-trapezoidal method: the Heun method, the improved Euler method, the modified Euler method, and the Runge-Kutta-2 method (RK2), the last of which which he prefers. He does not cover the Runge-midpoint method. This presentation of numerical methods is not as complete as ours. |
| Khan Academy: Euler's Method | Khan Academy video on the Euler method. It computes a few steps of the Euler method for the initial-value problem y' = y, y(0) = 1 with step size h = 1 and h = .5. This presentation of numerical methods is not as complete as ours. It does not cover the Runge-trapeziodal, Runge-midpoint, or Runge-Kutta methods. It does not cover the order of a method. |
| Khan Academy: Euler's Method Program Code | Khan Academy video on how to use its Euler method code. The code does fine for the initial-value problem y' = y, y(0) = 1, but has trouble for the initial-value problem y' = -x/y, y(0) = 8. It does not explain the source of the difficulty. |
| Khan Academy: Euler's Method Program Code | Link to the Khan Academy Euler method code used in the above video. We do not recommend using it. |
| Khan Academy: Example Euler's Method Exercise | Khan Academy video working out an exercise about the Euler method. Two steps of the Euler method are computed with step size h = 1 for the initial-value problem y' = 3 x - 2 y, y(0) = k. The step size is too large for the Euler method to behave well, so the exercise is somewhat academic. |