Get Math Help

Finite Difference Method

Solution plot

(using 10 steps with stepsize 0.17)

Stepwise results

step | x | y | local error | global error
0 | 0 | 2 | 0 | 0
⋮ | ⋮ | ⋮ | ⋮ | ⋮
10 | 1.7 | 0.0755396 | 0.0187996 | 0.0356128

Butcher tableau

1 |
| 1

Symbolic iteration code

y'(x) = f(x, y) = -2 x y(x), y(0) = 2
y_n + 1 = y_n + h k_1
x_n + 1 = x_n + h
k_1 = f(x_n, y_n)
k_2 = f(x_n + h, y_n + h k_1)
where y_0 = | 2
x_0 = | 0
h = | 0.17
n = | 0, ..., 10

Stability region in complex stepsize plane

stability function: z + 1

Exact solution of equation

y(x) = 2 e^(-x^2)

Stepsize comparison

Method comparison

Mathematica input

NDSolve[{y'[x] == -2 x y[x], y[0] == 2}, y, {x, 0, 1.7}, Method-> {"FixedStep", Method -> "ExplicitEuler"}, StartingStepSize -> 0.17, MaxStepFraction -> 1/10, WorkingPrecision -> MachinePrecision]

Why Club Z!?

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu.