Runge-Kutta method: Difference between revisions
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→{{header|J}}: typo
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NB. y is: y(ta) , ta , tb , tstep
NB. eg: fyp rk4 1 0 10 0.1
rk4=:
'Y0 a b h'=. 4{. y
T=. a + i.@>:&.(%&h) b - a
Line 231:
)</lang>
'''Example:'''
<lang j> fy=: (%16) * [: *: 4 + *: NB. f(t,y)
fyp=: (* %:)/ NB. f'(t,y)
report_whole=: (10 * i. >:10)&{ NB. report at whole-numbered t values
report_err=: (, {: - [: fy {.)"1 NB. report errors
report_err report_whole fyp
0 1 0
1 1.5625 _1.45722e_7
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9 451.562 _4.07232e_5
10 676 _5.09833e_5</lang>
=={{header|Mathematica}}==
<lang Mathematica>DSolve[{y'[t] == t * Sqrt[y[t]], y[0] == 1, y'[0] == 0}, y[t], t]//Simplify
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