95 lines
2.7 KiB
Go
95 lines
2.7 KiB
Go
// ODEMilneSimpson
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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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Milne-Simpson预估校正方法
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理论：
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预估：
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4h
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p_(k+1) = y_(k-3) + ---(2f_(k-2)-f_(k-1)+2fk)
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3
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校正：
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h
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y_(k+1) = y_(k-1) + ---(f_(k-1)+4fk+f_(k+1))
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3
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步长 h < 0.45/|fy(x,y)|
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四阶精度
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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 9.6.4
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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 初值,2x4
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h 步长
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n 积分步数
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输出 :
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sol 解矩阵
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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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// ODEMilneSimpson Milne-Simpson预估校正方法
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func ODEMilneSimpson(fun func(float64, float64) float64, x0 Matrix, h float64, n int) (Matrix, bool) {
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/*
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Milne-Simpson预估校正方法
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输入 :
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fun 被积分函数
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x0 初值,2x4
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h 步长
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n 积分步数
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输出 :
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sol 解矩阵
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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.ODEMilneSimpson: n is not a positive value")
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}
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//判断初值
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if (x0.Rows != 2) || (x0.Columns < 4) {
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panic("Error in goNum.ODEMilneSimpson: Initial values error")
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}
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sol := ZeroMatrix(2, n+1)
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p := ZeroMatrix(n+1, 1)
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var err bool = false
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//初值
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for i := 0; i < 4; i++ {
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sol.SetMatrix(0, i, x0.GetFromMatrix(0, i))
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sol.SetMatrix(1, i, x0.GetFromMatrix(1, i))
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}
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//计算
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for i := 4; i < n+1; i++ {
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sol.SetMatrix(0, i, sol.GetFromMatrix(0, i-1)+h) //xi
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//pi
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temp0 := fun(sol.GetFromMatrix(0, i-3), sol.GetFromMatrix(1, i-3)) //f_(i-3)
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temp1 := fun(sol.GetFromMatrix(0, i-2), sol.GetFromMatrix(1, i-2)) //f_(i-2)
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temp2 := fun(sol.GetFromMatrix(0, i-1), sol.GetFromMatrix(1, i-1)) //f_(i-1)
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soltemp := 2.0 * temp0
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soltemp += -1.0 * temp1
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soltemp += 2.0 * temp2
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p.SetMatrix(i, 0, sol.GetFromMatrix(1, i-4)+4.0*h*soltemp/3.0)
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//yi
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soltemp = temp1
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soltemp += 4.0 * temp2
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soltemp += fun(sol.GetFromMatrix(0, i), p.GetFromMatrix(i, 0)) //fi
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sol.SetMatrix(1, i, sol.GetFromMatrix(1, i-2)+h*soltemp/3.0)
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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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