80 lines
2.1 KiB
Go
80 lines
2.1 KiB
Go
// ODEHeun
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/*
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------------------------------------------------------
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作者 : Black Ghost
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日期 : 2018-12-26
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版本 : 0.0.0
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------------------------------------------------------
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常微分方程的Heun解法
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理论：
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对于常微分方程
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dy
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---- = f(x, y)
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dx
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y(x0) = y0, x0 <= x
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Heun法为
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1. p_(k+1) = yk+hf(xk,yk) //欧拉法
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2. y_(k+1) = yk+h(f(xk,yk)+f(x_(k+1),p_(k+1))/2 //梯形法
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k = 0,1,2,3,...
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参考：John H. Mathews and Kurtis D. Fink. Numerical
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methods using MATLAB, 4th ed. Pearson
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Education, 2004. ss 9.3
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------------------------------------------------------
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输入 :
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fun 被积分函数
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x0, y0 初值
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h 步长
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n 迭代次数
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输出 :
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sol 解矩阵，nx2
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err 解出标志：false-未解出或达到步数上限；
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true-全部解出
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------------------------------------------------------
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*/
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package goNum
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// ODEHeun 常微分方程的Heun解法
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func ODEHeun(fun func(float64, float64) float64, x0, y0, h float64, n int) (Matrix, bool) {
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/*
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常微分方程的Heun解法
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输入 :
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fun 被积分函数
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x0, y0 初值
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h 步长
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n 迭代次数
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输出 :
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sol 解矩阵，nx2
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err 解出标志：false-未解出或达到步数上限；
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true-全部解出
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*/
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//判断n
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if n < 0 {
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panic("Error in goNum.ODEHeun: n is not a positive value")
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}
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sol := ZeroMatrix(n+1, 2)
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p := ZeroMatrix(n+1, 2)
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var err bool = false
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//初值
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sol.SetMatrix(0, 0, x0)
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sol.SetMatrix(0, 1, y0)
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for i := 1; i < n+1; i++ {
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p.SetMatrix(i, 0, sol.GetFromMatrix(i-1, 0)+h) //xi=x_(i-1)+h
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sol.SetMatrix(i, 0, sol.GetFromMatrix(i-1, 0)+h) //xi=x_(i-1)+h
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soltemp := fun(sol.GetFromMatrix(i-1, 0), sol.GetFromMatrix(i-1, 1))
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p.SetMatrix(i, 1, sol.GetFromMatrix(i-1, 1)+h*soltemp)
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soltemp = h * (soltemp + fun(sol.GetFromMatrix(i, 0), p.GetFromMatrix(i, 1))) / 2.0
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sol.SetMatrix(i, 1, sol.GetFromMatrix(i-1, 1)+soltemp)
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}
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err = true
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return sol, err
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}
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