chapter9

library(mosaicCalc)

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library(mosaic)

library(mosaicCore)

library(mosaicData)

9.1 Solving differential equations

“Memecahkan” persamaan diferensial sama dengan menemukan nilai keadaan sebagai fungsi dari variabel bebas. Dalam “persamaan diferensial biasa”, hanya ada satu variabel bebas, biasanya disebut waktu. Dalam “persamaan diferensial parsial”, ada dua atau lebih variabel dependen, misalnya waktu dan ruang.

Fungsi tersebut integrateODE()menyelesaikan persamaan diferensial biasa yang dimulai dari kondisi awal keadaan tertentu.

"soln <- integrateODE(dx ~ r * x * (1 - x / K),
                     x = 1, K = 10, r = 0.5,
                     tdur = list(from=0, to=20))"

## [1] "soln <- integrateODE(dx ~ r * x * (1 - x / K),\n                     x = 1, K = 10, r = 0.5,\n                     tdur = list(from=0, to=20))"

Objek yang dibuat oleh integrateODE()adalah fungsi waktu. Atau, lebih tepatnya, ini adalah sekumpulan solusi, satu untuk setiap variabel keadaan. Dalam persamaan logistik, hanya ada satu variabel keadaan x .

"soln$x(0:5)"

## [1] "soln$x(0:5)"

Seringkali, Anda akan merencanakan solusi terhadap waktu:

"slice_plot(soln$x(t) ~ t, domain(t=0:20))"

## [1] "slice_plot(soln$x(t) ~ t, domain(t=0:20))"

Daftar Pustaka : https://dtkaplan.github.io/RforCalculus/dynamics.html