在Manipulate中绘制NDSolve

Question

我有以下工作Mathematica代码:

ODENInit[n_, xIni_] := 
    Join[{x[1][0] == xIni}, Table[x[i][0] == 0, {i, 2, n}]]
ODEN[n_] := 
    Join[{x[1]'[t] == k1 - k2 x[1][t]}, 
    Table[x[i]'[t] == k1 x[i - 1][t] - k2 x[i][t], {i, 2, n}]]
ODENVars[n_] := Table[x[i][t], {i, 1, n}];

Manipulate[
    Module[{sol}, 
        sol = NDSolve[
            Join[ODEN[10], ODENInit[10, 0]] /. {k1 -> mk1, k2 -> mk2}, 
                 ODENVars[10], {t, 0, 10}];
        Plot[Evaluate@Table[x[i][t] /. sol, {i, 1, 10}], {t, 0, 10}]], 
    {{mk1, 1}, 0.1, 10, .1}, {{mk2, 1}, 0.1, 10, .1}]

有没有办法重写Manipulate部分,这样我就不需要将k1和k2参数重新分配给虚拟参数,这里是mk1和mk2？感谢任何提前提示.

Answer 1

是的,只要让它们成为函数的参数ODEN.还有几点要改进代码:

1)通过Initialization引入函数使代码自我可靠

3)ControlType -> None用于引入虚拟本地化变量以避免额外的Module内部manipulate- 因为无论如何围绕其内容进行Manipulate包装DynamicModule.

Manipulate[

 sol = NDSolve[Join[ODEN[10, k1, k2], ODENInit[10, 0]], 
   ODENVars[10], {t, 0, 10}];

 Plot[Evaluate@Table[x[i][t] /. sol, {i, 1, 10}], {t, 0, 10}],

 {{k1, 1}, 0.1, 10, .1},
 {{k2, 1}, 0.1, 10, .1},
 {sol, ControlType -> None},

 Initialization :> {

   ODENInit[n_, xIni_] := 
    Join[{x[1][0] == xIni}, Table[x[i][0] == 0, {i, 2, n}]],

   ODEN[n_, k1_, k2_] := 
    Join[{x[1]'[t] == k1 - k2 x[1][t]}, 
     Table[x[i]'[t] == k1 x[i - 1][t] - k2 x[i][t], {i, 2, n}]],

   ODENVars[n_] := Table[x[i][t], {i, 1, n}]

   }]

要回答你的评论,如果你真的倾向于k在函数之外保持全局定义,那么这将做:

Manipulate[

 Block[{sol, k1 = mk1, k2 = mk2},
  sol = NDSolve[Join[ODEN[10], ODENInit[10, 0]], 
    ODENVars[10], {t, 0, 10}];
  Plot[Evaluate@Table[x[i][t] /. sol, {i, 1, 10}], {t, 0, 10}]],

 {{mk1, 1}, 0.1, 10, .1}, {{mk2, 1}, 0.1, 10, .1}]