WOLFRAM

Wolfram 语言与系统参考资料中心

InitialSeeding

是 NDSolve 和其他函数的一个选项，对用来指定迭代算法可能使用的变量的初始种子值的方程式进行指定.

更多信息
Details and Options Details and Options
范例  
基本范例  
范围  
可能存在的问题  
参见
技术笔记
历史
按以下格式引用：

InitialSeeding

InitialSeeding

是 NDSolve 和其他函数的一个选项，对用来指定迭代算法可能使用的变量的初始种子值的方程式进行指定.

更多信息

  • 对于 NDSolve 和其他函数中的微分代数方程，InitialSeeding->{u[t0]==val} 表明应使用数值 val 来求得一致的初始条件.
  • 对于 NDSolve 和其他函数中的静态非线性偏微分方程，InitialSeeding->{u[x1,…]==fun[x1,…]} 表明应使用自变量为 x1,… 的数值函数 fun 来获取网格的初始向量.
  • 不同的初始种子值可能会导致不同的解. »

范例

打开所有单元 关闭所有单元

基本范例  (1)

为边界值问题指定初始种子 0：

Wolfram Language code: NDSolveValue[{-2 u[x] Derivative[1][u][x] - Derivative[2][u][x] == 1, DirichletCondition[u[x] == 0, x == 0], DirichletCondition[u[x] == 0, x == 1]}, u, {x}∈Line[{{0}, {1}}], InitialSeeding -> {u[x] == 0}]

范围  (7)

指定取决于空间坐标的初始种子：

Wolfram Language code: NDSolveValue[{-2 u[x] Derivative[1][u][x] - Derivative[2][u][x] == 0, DirichletCondition[u[x] == 0, x == 0], DirichletCondition[u[x] == 1, x == 1]}, u, {x}∈Line[{{0}, {1}}], InitialSeeding -> {u[x] == x}]

使用线性边界值问题的解作为非线性边界值问题的初始种子：

Wolfram Language code: linear = NDSolveValue[{-2 u[x] - Derivative[2][u][x] == 0, DirichletCondition[u[x] == 0, x == 0], DirichletCondition[u[x] == 1, x == 1]}, u, {x}∈Line[{{0}, {1}}]]
Wolfram Language code: NDSolveValue[{-2 u[x] Derivative[1][u][x] - Derivative[2][u][x] == 0, DirichletCondition[u[x] == 0, x == 0], DirichletCondition[u[x] == 1, x == 1]}, u, {x}∈Line[{{0}, {1}}], InitialSeeding -> {u[x] == linear[x]}]

InitialSeeding 的不同设置可能会得到边界值问题不同的解：

Wolfram Language code: eqn = Inactive[Div][{{1 / 100, 0}, {0, 1 / 100}}. Inactive[Grad][u[x, y], {x, y}], {x, y}] - (u[x, y] ^ 3 - u[x, y]) == 0; ifun = NDSolveValue[{eqn, DirichletCondition[u[x, y] == 0, True]}, u, {x, y}∈Rectangle[{-1, -1}, {1, 1}], InitialSeeding -> {u[x, y] == 0}]; Plot3D[ifun[x, y], {x, y}∈Rectangle[{-1, -1}, {1, 1}]]

为 StartingGuess 指定不同的值：

Wolfram Language code: ifun = NDSolveValue[{eqn, DirichletCondition[u[x, y] == 0, True]}, u, {x, y}∈Rectangle[{-1, -1}, {1, 1}], InitialSeeding -> {u[x, y] == 1}]; Plot3D[ifun[x, y], {x, y}∈Rectangle[{-1, -1}, {1, 1}]]

指定复数作为初始种子：

Wolfram Language code: NDSolveValue[{Inactive[Plus][Inactive[Div][-Inactive[Grad][u[x], {x}], {x}], u[x] ^ 3] == 0, DirichletCondition[u[x] == 0, True]}, u, {x}∈Line[{{0}, {1}}], InitialSeeding -> {u[x] == 0.I}]

求边界值问题的解：

Wolfram Language code: solution1 = NDSolveValue[{-Derivative[1][u][x] - x Derivative[2][u][x] == E^u[x] x, DirichletCondition[u[x] == 0, x == 1]}, u, Element[{x}, Line[{{0}, {1}}]], InitialSeeding -> {u[x] == 1}]
Wolfram Language code: Plot[solution1[x], {x, 0, 1}, PlotRange -> All]

通过设置不同的 InitialSeeding 求不同的解：

Wolfram Language code: solution2 = NDSolveValue[{-Derivative[1][u][x] - x Derivative[2][u][x] == E^u[x] x, DirichletCondition[u[x] == 0, x == 1]}, u, Element[{x}, Line[{{0}, {1}}]], InitialSeeding -> {u[x] == -4x + 4}]
Wolfram Language code: Plot[solution2[x], {x, 0, 1}, PlotRange -> All]

对于非线性边界值问题，为 "Shooting" 方法设置不同的初始种子：

Wolfram Language code: pfun = ParametricNDSolveValue[{x''[t] + Sin[x[t]] == 0, x[0] == x[10] == 0}, x, t, s, Method -> "Shooting", InitialSeeding -> {x'[0] == s}]
Wolfram Language code: Plot[{pfun[1.5][t], pfun[1.75][t], pfun[2.][t]}, {t, 0, 10}, PlotStyle -> {Red, Blue, Green}]

对于 "Shooting" 方法，初始种子也可以在解的区间内：

Wolfram Language code: mid = NDSolveValue[{x''[t] + Sin[x[t]] == 0, x[0] == x[10] == 0}, x, t, InitialSeeding -> {x[5] == 0, x'[5] == -2}]; Plot[mid[t], {t, 0, 10}]

用 InitialSeeding 来求微分代数方程组的一致初始条件：

Wolfram Language code: sol = NDSolve[{Subscript[x, 1]'[t] == Subscript[x, 3][t], Subscript[x, 2][t](1 - Subscript[x, 2][t]) == 0, Subscript[x, 1][t] Subscript[x, 2][t] + Subscript[x, 3][t] (1 - Subscript[x, 2][t]) == t, Subscript[x, 1][0] == 1}, {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3]}, {t, 0, 1}, InitialSeeding -> {Subscript[x, 2][0] == 0}];
Wolfram Language code: Plot[Evaluate[{Subscript[x, 1][t], Subscript[x, 3][t]} /. First[sol]], {t, 0, 1}, PlotStyle -> {Red, Blue}]

可能存在的问题  (2)

对于有些 DAE 方程组，如果未指定初始种子，可能会发出有关初始条件不一致的消息：

Wolfram Language code: sol = NDSolve[{Subscript[x, 1]'[t] == Subscript[x, 3][t], Subscript[x, 2][t](1 - Subscript[x, 2][t]) == 0, Subscript[x, 1][t] Subscript[x, 2][t] + Subscript[x, 3][t] (1 - Subscript[x, 2][t]) == t, Subscript[x, 1][0] == 1}, {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3]}, {t, 0, 1}];
Wolfram Language code: Plot[Evaluate[{Subscript[x, 1][t], Subscript[x, 3][t]} /. First[sol]], {t, 0, 1}, PlotStyle -> {Red, Blue}]

提供初始条件种子以获取一致的初始条件：

Wolfram Language code: sol = NDSolve[{Subscript[x, 1]'[t] == Subscript[x, 3][t], Subscript[x, 2][t](1 - Subscript[x, 2][t]) == 0, Subscript[x, 1][t] Subscript[x, 2][t] + Subscript[x, 3][t] (1 - Subscript[x, 2][t]) == t, Subscript[x, 1][0] == 1}, {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3]}, {t, 0, 1}, InitialSeeding -> {Subscript[x, 2][0] == 0}];
Wolfram Language code: Plot[Evaluate[{Subscript[x, 1][t], Subscript[x, 3][t]} /. First[sol]], {t, 0, 1}, PlotStyle -> {Red, Blue}]

不同的初始种子值可能会导向 DAE 方程组的不同结果：

Wolfram Language code: pendulumDAE = (⁠| | | ---------------------- | | x''[t] == x[t] λ[t] | | y''[t] == y[t] λ[t] - 1 | | x[t]^2 + y[t]^2 == 1 |⁠) ;
Wolfram Language code: sol = NDSolve[{pendulumDAE, y'[0] == 1, x'[0] == 0}, {x, y, λ}, {t, 0, 10}, Method -> {"IndexReduction" -> Automatic, "DAEInitialization" -> "Collocation"}, InitialSeeding -> {x[0] == 1}]; Plot[Evaluate[{x[t], y[t]} /. First[sol]], {t, 0, 10}]

指定不同的初始点：

Wolfram Language code: sol = NDSolve[{pendulumDAE, y'[0] == 1, x'[0] == 0}, {x, y, λ}, {t, 0, 10}, Method -> {"IndexReduction" -> Automatic, "DAEInitialization" -> "Collocation"}, InitialSeeding -> {x[0] == -1}]; Plot[Evaluate[{x[t], y[t]} /. First[sol]], {t, 0, 10}]
Wolfram Research (2019)，InitialSeeding，Wolfram 语言函数，https://reference.wolfram.com/language/ref/InitialSeeding.html.

文本

Wolfram Research (2019)，InitialSeeding，Wolfram 语言函数，https://reference.wolfram.com/language/ref/InitialSeeding.html.

CMS

Wolfram 语言. 2019. "InitialSeeding." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/InitialSeeding.html.

APA

Wolfram 语言. (2019). InitialSeeding. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/InitialSeeding.html 年

BibTeX

@misc{reference.wolfram_2026_initialseeding, author="Wolfram Research", title="{InitialSeeding}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/InitialSeeding.html}", note=[Accessed: 10-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_initialseeding, organization={Wolfram Research}, title={InitialSeeding}, year={2019}, url={https://reference.wolfram.com/language/ref/InitialSeeding.html}, note=[Accessed: 10-November-2026]}