matlab project submit your elms mor.ru xsep 17, 2020 · matlab project submission submit your code...
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MATLAB project submission
Submit your code to ELMS mor.ru x
marhproblem bycomment outpnt section
E In the absence of predators rats grow exponentially
and double their population every 3 years Initiallythere are 20000 rats and they are eaten by predators
at a rate of 3000 per year What is the population
of rats after 6 years
no predators 㖲 r p r
p l t I e t p10 1
P 13 2 P Piee 23 r l n 2 r
with predators i 桇 r p h l t
装 f p 3000
linear ODE you can also do separable
装 f p 3000
alt Y Alt 11 Y dt ftintegrating factor ieftftletpk 3ooefte
tpm efpifl oooe
sjdse.it30001今 s__
器 e i 1
ént P 器 e 哭 1
Pit P e t器 1 e的
P 20000
in 6 2000 ⼼ 2㙄 11 巴以9
o Logistic model i
桇 Rlplp h.lt
R l p r a p r so as o
7Youth rate L when pT
similar toeyp growth restriction from environment
㖲 r a p p when no harvest
autonomous
eq.glp r a p p r 1 1 f l p r11 炎 p
h f sophase portrait i
g 0 o
o kunstable stable
hi Ccrryinsy of the ecosystem
1.7 Numerical methods
if It y y It ⼆ I
want to solve on t E Et I tFIp exact soI'm Y It1
i1ifi i
i i 1 1ihh.in i.i st.tl ˊ____ tN1
ti t Fit Nto
u Discretinnne iti.it ⻔t t.at at r____ t 灬 t t F
uniform time steps i h E n h n 0,1.2 NtF t Ih N stepsie.se
Design formula to get It n yn n 0 li
Nyuapproximates Y Hn
Explicit Euler method
Y It f It Y It IYltthl YHIYltthl Yl.tlY ⼼ ⼆点 x
⼀ ⼆h
if his small
YltthI Ylti
tflt.YltilYltthJEYltlthflt.Yltilevalnate
t
tnYltnt.IE Yltn h f Itn Yltn
explicit Enter method
y n_n ⼆ ynthfltniynl.n.co I
y ⼆ ⼆
⼆ Solve y f y E y l n 2
by explicit Enter method w h 0.1
to approximate Y 1 2 1the exact soI 1
to 1 t 1.1 tz 1.2
y 2
y y h f to y 2 0.11 f 2 12 23
y y thflt.it 2.3 1 011只以 药⽅
I compare ul exact sok Y It P 3⽇ ㄚ 11.2 2.592____
Global error Y It ㄧ y N
Localerrorzren i when substitute Yin into
numerical method the error you have
For explicit Euler
local error is Yltntil Yltnl hfltn.YHnll
YHntni ltn.li啊O h
us expect global error EN Olli O l h
h t N toexplicit Euler is firsforderaccurate_r.cor moregenerally when global error is Ollithen the method is math order accurate