如何修复Adam的方法？

Question

我有这样的错误：

  

坐标..不是浮点数

并无法正确修复它。

该程序适用于函数1 - t *y，但不适用于y*y*Exp[t] - 2*y。

如果你告诉我为什么以及如何解决这个问题，我将非常高兴。

    ABM[a0_, b0_, \[Alpha]_, m0_] := 
  Module[{a = a0, b = b0, F, j, k, m = m0, p}, 
       h = (b - a)/m; T = Table[a, {m + 1}]; 
   Y = Table[\[Alpha], {m + 1}]; 
        For[j = 1, j <= 3, j++, Subscript[k, 1] = h*f[T[[j]], Y[[j]]]; 

    Subscript[k, 2] = h*f[T[[j]] + h/2, Y[[j]] + Subscript[k, 1]/2]; 

    Subscript[k, 3] = h*f[T[[j]] + h/2, Y[[j]] + Subscript[k, 2]/2]; 

    Subscript[k, 4] = h*f[T[[j]] + h, Y[[j]] + Subscript[k, 3]]; 

    Y[[j + 1]] = Y[[j]] + (1/6)*(Subscript[k, 1] + 2*Subscript[k, 2] + 
                    2*Subscript[k, 3] + Subscript[k, 4]); 
    T[[j + 1]] = a + h*j; ]; 
        Subscript[F, 0] = f[T[[1]], Y[[1]]]; Subscript[F, 1] = 
          f[T[[2]], Y[[2]]]; Subscript[F, 2] = f[T[[3]], Y[[3]]]; 
        Subscript[F, 3] = f[T[[4]], Y[[4]]]; For[j = 4, j <= m, j++, 

    p = Y[[j]] + (h/24)*(-9*Subscript[F, 0] + 37*Subscript[F, 1] - 
                    59*Subscript[F, 2] + 55*Subscript[F, 3]); 
           T[[j + 1]] = a + h*j; 
    p = Y[[j]] + (h/24)*(Subscript[F, 1] - 
                    5*Subscript[F, 2] + 19*Subscript[F, 3] + 
         9*f[T[[j + 1]], p]); 
           Y[[j + 1]] = p; Subscript[F, 0] = Subscript[F, 1]; 
           Subscript[F, 1] = Subscript[F, 2]; Subscript[F, 2] = 
             Subscript[F, 3]; 
    Subscript[F, 3] = f[T[[j + 1]], Y[[j + 1]]]; ]; 
        Return[Transpose[{T, Y}]]]; 
f[t_, y_] = y*y*Exp[t] - 2*y; 
Print["Find numerical solutions to the D.E."]; 
Print["y' = ", f[t, y]]; 
n = 25; 
pts1 = ABM[0, 8, 2., n]; 
Y1 = Y; 
Needs["Graphics`Colors`"]; 
graph1 = ListPlot[pts1, PlotJoined -> True, PlotStyle -> Green, 
       PlotRange -> {{0, 10}, {0, 10}}]; 
Print["The Adams-Bashforth-Moulton solution for  y' = ", f[t, y]]; 
Print["Using  n = ", n + 1, "  points."]; 
Print[pts1]; 
Print[""]; 
Print["The final value is  y(5) = ", Subscript[y, n + 1], " = ", 
     Y[[n + 1]]];