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rkClassicClass.lua
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-- Lua & TI-Nspire による常微分方程式の数値解法 / 古典的ルンゲクッタ法 | |
rkClassic = class() | |
function rkClassic:init(funcs, t0, inits, h, numOfDiv) | |
self.Unpack = unpack or table.unpack | |
self.funcs = funcs | |
self.t0 = t0 | |
self.inits = inits | |
self.dim = #funcs | |
self.numOfDiv = numOfDiv or 1 | |
self.h = h / self.numOfDiv | |
self.f = {{}, {}, {}, {}} | |
self.temp = {{}, {}, {}} | |
end | |
function rkClassic:updateRK() | |
for i = 1, self.numOfDiv do | |
for j = 1, self.dim do self.f[1][j] = self.funcs[j](self.t0 , self.Unpack(self.inits)) ; self.temp[1][j] = self.inits[j] + self.h/2 * self.f[1][j] end | |
for j = 1, self.dim do self.f[2][j] = self.funcs[j](self.t0 + self.h/2, self.Unpack(self.temp[1])) ; self.temp[2][j] = self.inits[j] + self.h/2 * self.f[2][j] end | |
for j = 1, self.dim do self.f[3][j] = self.funcs[j](self.t0 + self.h/2, self.Unpack(self.temp[2])) ; self.temp[3][j] = self.inits[j] + self.h * self.f[3][j] end | |
for j = 1, self.dim do self.f[4][j] = self.funcs[j](self.t0 + self.h , self.Unpack(self.temp[3])) end | |
for j = 1, self.dim do self.inits[j] = self.inits[j] + self.h/6 * (self.f[1][j] + 2 * (self.f[2][j] + self.f[3][j]) + self.f[4][j]) end | |
self.t0 = self.t0 + self.h | |
end | |
return self | |
end | |
function rkClassic:print() | |
print(self.t0, "{"..table.concat(self.inits, ", ").."}") | |
return self | |
end | |
--- 確かめる。 | |
do | |
-- この聯立微分方程式を解く。 | |
local function xDot(t, x, y) return y end -- x'(t) = y(t) | |
local function yDot(t, x, y) return t - x end -- y'(t) = t - x(t) | |
-- インスタンス化して、 | |
local rk = rkClassic({xDot, yDot}, 0, {0, 0}, 0.25, _) -- (函数リスト, t0, 初期値リスト, 刻み幅 [, 内部分割数]) | |
-- 必要な回数だけそのインスタンスを更新し、更新するたびに print して確認する。 | |
for i = 1, 30 do | |
rk:updateRK():print() | |
end | |
end |
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