I tried running the following codes but got error

restart;
Digits := 30:

f1 := proc(n)
    lamda * y1[n] + (y2[n])^2;
end proc:

f2 := proc(n)
    -y2[n];
end proc:

F1 := proc(n)
    lamda * f1(n) + 2 * f2(n) * y2[n];
end proc:

F2 := proc(n)
    -f2(n);
end proc:

e1 := y1[n+2] = (53/485) * y1[n] - (6/485) * F1(n+2) * h^2 + (6/485) * f1(n) * h +
                     (128/485) * f1(n+1/2) * h + (384/485) * f1(n+3/2) * h +
                     (432/485) * f1(n+1) * h + (20/97) * f1(n+2) * h +
                     (432/485) * y1[n+1] + (512/485) * y1[n+1/2] - (512/485) * y1[n+3/2]:

e2 := h^2 * F1(n+1/2) = -(9/970) * F1(n+2) * h^2 + (503/1940) * f1(n) * h -
                           (9412/1455) * f1(n+1/2) * h - (682/485) * f1(n+3/2) * h -
                           (4041/485) * f1(n+1) * h + (83/1164) * f1(n+2) * h +
                           (3878/1455) * y1[n] + (9054/485) * y1[n+1] -
                           (14166/485) * y1[n+1/2] + (11458/1455) * y1[n+3/2]:

e3 := h^2 * F1(n+1) = -(28/4365) * F1(n+2) * h^2 + (541/8730) * f1(n) * h +
                         (25072/13095) * f1(n+1/2) * h - (5968/4365) * f1(n+3/2) * h +
                         (224/485) * f1(n+1) * h + (269/5238) * f1(n+2) * h +
                         (7532/13095) * y1[n] - (9476/485) * y1[n+1] +
                         (4864/485) * y1[n+1/2] + (116992/13095) * y1[n+3/2]:

e4 := h^2 * F1(n+3/2) = -(31/970) * F1(n+2) * h^2 + (671/5820) * f1(n) * h +
                           (3902/1455) * f1(n+1/2) * h + (12676/1455) * f1(n+3/2) * h +
                           (5481/485) * f1(n+1) * h + (329/1164) * f1(n+2) * h +
                           (1502/1455) * y1[n] + (9846/485) * y1[n+1] +
                           (5526/485) * y1[n+1/2] - (47618/1455) * y1[n+3/2]:

e5 := y2[n+2] = (53/485) * y2[n] - (6/485) * F2(n+2) * h^2 + (6/485) * f2(n) * h +
                     (128/485) * f2(n+1/2) * h + (384/485) * f2(n+3/2) * h +
                     (432/485) * f2(n+1) * h + (20/97) * f2(n+2) * h +
                     (432/485) * y2[n+1] + (512/485) * y2[n+1/2] - (512/485) * y2[n+3/2]:

e6 := h^2 * F2(n+1/2) = -(9/970) * F2(n+2) * h^2 + (503/1940) * f2(n) * h -
                           (9412/1455) * f2(n+1/2) * h - (682/485) * f2(n+3/2) * h -
                           (4041/485) * f2(n+1) * h + (83/1164) * f2(n+2) * h +
                           (3878/1455) * y2[n] + (9054/485) * y2[n+1] -
                           (14166/485) * y2[n+1/2] + (11458/1455) * y2[n+3/2]:

e7 := h^2 * F2(n+1) = -(28/4365) * F2(n+2) * h^2 + (541/8730) * f2(n) * h +
                         (25072/13095) * f2(n+1/2) * h - (5968/4365) * f2(n+3/2) * h +
                         (224/485) * f2(n+1) * h + (269/5238) * f2(n+2) * h +
                         (7532/13095) * y2[n] - (9476/485) * y2[n+1] +
                         (4864/485) * y2[n+1/2] + (116992/13095) * y2[n+3/2]:

e8 := h^2 * F2(n+3/2) = -(31/970) * F2(n+2) * h^2 + (671/5820) * f2(n) * h +
                           (3902/1455) * f2(n+1/2) * h + (12676/1455) * f2(n+3/2) * h +
                           (5481/485) * f2(n+1) * h + (329/1164) * f2(n+2) * h +
                           (1502/1455) * y2[n] + (9846/485) * y2[n+1] +
                           (5526/485) * y2[n+1/2] - (47618/1455) * y2[n+3/2]:

Digits := 30: lamda := 10000:
h := 0.1:
N := solve(h*p = 10/4, p):
n := 0:
exy1 := [seq](eval(-exp(-2*i/2)/(lamda+2)), i = h .. N, h):
exy2 := [seq](eval(exp(-i/2)), i = h .. N, h):

iny1 := 1:
iny2 := 1:

c := 1:
vars := y1[n+1/2], y1[n+1], y1[n+3/2], y1[n+2], y2[n+1/2], y2[n+1], y2[n+3/2], y2[n+2]:

printf("%6s%15s%15s%15s%15s%10s%10s\n", 
    "h", "numy1", "numy2", 
    "exy1", "exy2", 
    "erry1", "erry2");

tolerance := 1e-6:
st := time():
for k from 1 to N do

    res := eval(<vars>, fsolve(eval({e||(1..8)}, [y1[n]=iny1, y2[n]=iny2]), {vars}), tolerance = tolerance):

    for i from 1 to 4 do
        printf("%6.5f%15.10f%15.10f%15.8g%15.10g%10.3g%10.3g\n", 
        h*c, res[i], res[i+4], 
        exy1[c], exy2[c], 
        abs(res[i]-exy1[c]), abs(res[i+4]-exy2[c])):

        c := c+1:
    end do:
    iny1 := res[4]:
    iny2 := res[8]:
end do:
v := time() - st:
 

Dear all,

Please I want to solve the following boundary value problem numerically with the attached code

y''=((y')^2+y^2)/(2*exp(x)),      0<x<1

with boundary conditions as follows

y(0)-y'(0)=0, y(1)+y'(1)=2*exp(1)

The exact solution is y(x)=exp(x).

How do I modify the code to be able to handle it?

Please the delta in the code represents y'.

Thank you for your time and best regards

Download K2_Prob_4_direct_2nd_derivative.mw

Dear esteem Colleagues,

Please how do I modify the following two files (though similar) to get consistent errors? I am not sure where I made the mistake.

Any modifications would be appreciated.

Thank you all for your time and mentorship. Best regard

Biratu_Mapleprimes.mw

DDE_2_Mapleprime.mw

Dear respected colleagues,

The first "ex 1" and second "non linear" codes were sent to me by a colleague. It would be appreciated if they can be modified to look like the one saved with "K2 Nonlinear_Fang 2009". Thank you all for your time and best regards.

ex1.mw

non_linear.mw

K2_Nonlinear_Fang_2009.mw

Dear esteem colleagues,

Please I am trying to plot a function using both implicitplot and contourplot. However, I found out that I have two different plots. What are the differences between them and perhaps which is better?

Thank you all for your time and best regards.