Question

b) Solve the IVP, ; )4(y 4
x 4y
1
y
2
=
−
′ = using Euler’s method. Find )2.4(y with h = 2.0
and 1.0 and extrapolate the value )

Answer 1

Answer on Question #60836 – Math – Algorithms | Quantitative Methods

Question

b) Solve the IVP, ; )4(y 4

x 4y

1

y

2

=

-

' = using Euler's method. Find )2.4(y with h = 2.0

and 1.0 and extrapolate the value )

Solution

By Euler's method

$$y_{n+1} = y_n + f(x_n, y_n) \cdot h,$$

where

$$f = y' = \frac{1}{x^2 - 4y}, \quad h = x_{n+1} - x_n$$

We have starting points $y(4) = 4$:

$$y_0 = 4, \quad x_0 = 4.$$

Let's find first approximation:

$$f(x_0, y_0) = \frac{1}{16 - 16} = [\infty]$$

So we cannot solve the IVP by Euler's method, because $f(x,y)$ at first approximation is infinity.

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