Chapter D1.2, Problem 45E

Euler’s method on more general grids Suppose the solution of the initial value problem $y^{\prime }\left(t\right)=f\left(t,y\right),y\left(a\right)=A$ is to be approximated on the interval [a, b].

  a.    If N + 1 grid points are used (including the endpoints), what is the time step  Δt?

  b.    Write the first step of Euler’s method to compute u₁.

  c.    Write the general step of Euler’s method that applies, for k = 0,1,…, N – 1.