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Expression 16:
16
Expression 17:
17
Cool RK4 Implementation
Cool RK4 Implementation
18
Rutta Kunda
Rutta Kunda
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19
Takes in point and gives you derivative at that point
Takes in point and gives you derivative at that point
20
Expression 21: "F" Subscript, 0 , Baseline left parenthesis, "p" Subscript, 0 , Baseline , right parenthesis equals "f" left parenthesis, "p" Subscript, 0 , Baseline . "x" , "p" Subscript, 0 , Baseline . "y" , right parenthesis
F
0
p
0
=
f
p
0
.
x
,
p
0
.
y
21
Desmos does not have variables, so you need to do this weird stuff to speed up RK4 math
Desmos does not have variables, so you need to do this weird stuff to speed up RK4 math
22
This uses the 3/8ths rule to remove as much error as possible while still being fairly fast.
This uses the 3/8ths rule to remove as much error as possible while still being fairly fast.
23
Expression 24: "k" left parenthesis, "p" Subscript, 0 , Baseline , "h" Subscript, 0 , Baseline , right parenthesis equals "k" Subscript, 1 , Baseline left parenthesis, "p" Subscript, 0 , Baseline , "h" Subscript, 0 , Baseline , "h" Subscript, 0 , Baseline left parenthesis, "F" Subscript, 0 , Baseline left parenthesis, "p" Subscript, 0 , Baseline , right parenthesis , right parenthesis , right parenthesis
k
p
0
,
h
0
=
k
1
p
0
,
h
0
,
h
0
F
0
p
0
24
Expression 25: "k" Subscript, 1 , Baseline left parenthesis, "p" Subscript, 0 , Baseline , "h" Subscript, 0 , Baseline , "K" Subscript, 1 , Baseline , right parenthesis equals "k" Subscript, 2 , Baseline left parenthesis, "p" Subscript, 0 , Baseline , "h" Subscript, 0 , Baseline , "K" Subscript, 1 , Baseline , "h" Subscript, 0 , Baseline "F" Subscript, 0 , Baseline left parenthesis, "p" Subscript, 0 , Baseline plus StartFraction, "K" Subscript, 1 , Baseline Over 3 , EndFraction , right parenthesis , right parenthesis
k
1
p
0
,
h
0
,
K
1
=
k
2
p
0
,
h
0
,
K
1
,
h
0
F
0
p
0
+
K
1
3
25
Expression 26: "k" Subscript, 2 , Baseline left parenthesis, "p" Subscript, 0 , Baseline , "h" Subscript, 0 , Baseline , "K" Subscript, 1 , Baseline , "K" Subscript, 2 , Baseline , right parenthesis equals "k" Subscript, 3 , Baseline left parenthesis, "p" Subscript, 0 , Baseline , "h" Subscript, 0 , Baseline , "K" Subscript, 1 , Baseline , "K" Subscript, 2 , Baseline , "h" Subscript, 0 , Baseline "F" Subscript, 0 , Baseline left parenthesis, "p" Subscript, 0 , Baseline minus StartFraction, "K" Subscript, 1 , Baseline Over 3 , EndFraction plus "K" Subscript, 2 , Baseline , right parenthesis , right parenthesis
k
2
p
0
,
h
0
,
K
1
,
K
2
=
k
3
p
0
,
h
0
,
K
1
,
K
2
,
h
0
F
0
p
0
−
K
1
3
+
K
2
26
Expression 27: "k" Subscript, 3 , Baseline left parenthesis, "p" Subscript, 0 , Baseline , "h" Subscript, 0 , Baseline , "K" Subscript, 1 , Baseline , "K" Subscript, 2 , Baseline , "K" Subscript, 3 , Baseline , right parenthesis equals "p" Subscript, 0 , Baseline plus StartFraction, "K" Subscript, 1 , Baseline plus 2 "K" Subscript, 2 , Baseline plus 3 "K" Subscript, 3 , Baseline plus "h" Subscript, 0 , Baseline "F" Subscript, 0 , Baseline left parenthesis, "p" Subscript, 0 , Baseline plus "K" Subscript, 1 , Baseline minus "K" Subscript, 2 , Baseline plus "K" Subscript, 3 , Baseline , right parenthesis Over 8 , EndFraction
k
3
p
0
,
h
0
,
K
1
,
K
2
,
K
3
=
p
0
+
K
1
+
2
K
2
+
3
K
3
+
h
0
F
0
p
0
+
K
1
−
K
2
+
K
3
8
27
Solution Line
Solution Line
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28
Vector Field Config
Vector Field Config
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32
Vector Field
Vector Field
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36
Expression 48:
48
49
powered by
powered by
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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