27 lines
749 B
Plaintext
27 lines
749 B
Plaintext
# Declaration for the sake of euler_table()
|
|
create or replace function cooling(x,y) as NULL;
|
|
|
|
# Euler method assuming cooling/2 is available
|
|
create or replace function euler_table(x_start, y_start, x2, h) as table (
|
|
with recursive cte as (
|
|
select x_start::DOUBLE as x, y_start::DOUBLE as y
|
|
union all
|
|
select x + h as x,
|
|
y + h*cooling(x, y)
|
|
from cte
|
|
where (x < x2 and x_start < x2) or
|
|
(x > x2 and x_start > x2)
|
|
)
|
|
from cte
|
|
);
|
|
|
|
create or replace function euler(x_start, y_start, x2, h) as (
|
|
select last(y order by x) from euler_method(x_start, y_start, x2, h)
|
|
);
|
|
|
|
## Example:
|
|
create or replace function cooling(x,y) as
|
|
-0.07 * (y - 20);
|
|
|
|
select h, euler(0,100, 100, h) from unnest([1,2,5,10,20]) _(h);
|