Desmos Vector Field

運算式 16:

運算式 17:

Cool RK4 Implementation

Rutta Kunda

Takes in point and gives you derivative at that point

運算式 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

Desmos does not have variables, so you need to do this weird stuff to speed up RK4 math

This uses the 3/8ths rule to remove as much error as possible while still being fairly fast.

運算式 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

運算式 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

運算式 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

運算式 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

Solution Line

Vector Field Config

Vector Field

運算式 48:

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