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.

Hello everyone,

While trying to open a maple document, a box pops up with the text "How do you want to open this file?" with the options "Maple Text, Plain Text, Maple Inputs" what could be responsible for this? and which of the options is better for mathematics and coding?

Thank you so much

restart;
Digits:=30:

f:=proc(n)
	x[n]-y[n];
	
end proc:


e1:=y[n] = (15592/1575)*h*f(n+5)+(35618816/99225)*h*f(n+9/2)-(4391496/15925)*h*f(n+13/3)-(2035368/13475)*h*f(n+14/3)-(212552/121275)*h*f(n+1)+(10016/11025)*h*f(n+2)-(31672/4725)*h*f(n+3)+(19454/315)*h*f(n+4)-(351518/1289925)*h*f(n)+y[n+4]:
e2:=y[n+1] = -(34107/22400)*h*f(n+5)-(212224/3675)*h*f(n+9/2)+(92569149/2038400)*h*f(n+13/3)+(82333989/3449600)*h*f(n+14/3)-(568893/1724800)*h*f(n+1)-(459807/313600)*h*f(n+2)+(1189/22400)*h*f(n+3)-(50499/4480)*h*f(n+4)+(32951/6115200)*h*f(n)+y[n+4]:
e3:=y[n+2] = (69/175)*h*f(n+5)+(1466368/99225)*h*f(n+9/2)-(13851/1225)*h*f(n+13/3)-(60507/9800)*h*f(n+14/3)+(43/3675)*h*f(n+1)-(3509/9800)*h*f(n+2)-(6701/4725)*h*f(n+3)+(871/420)*h*f(n+4)-(247/396900)*h*f(n)+y[n+4]:
e4:=y[n+3] = -(31411/201600)*h*f(n+5)-(745216/99225)*h*f(n+9/2)+(13557213/2038400)*h*f(n+13/3)+(9737253/3449600)*h*f(n+14/3)-(20869/15523200)*h*f(n+1)+(36329/2822400)*h*f(n+2)-(202169/604800)*h*f(n+3)-(100187/40320)*h*f(n+4)+(14669/165110400)*h*f(n)+y[n+4]:
e5:=y[n+13/3] = -(3364243/1322697600)*h*f(n+5)-(134364928/651015225)*h*f(n+9/2)+(19955023/55036800)*h*f(n+13/3)+(5577703/93139200)*h*f(n+14/3)-(910757/101847715200)*h*f(n+1)+(1336457/18517766400)*h*f(n+2)-(2512217/3968092800)*h*f(n+3)+(31844549/264539520)*h*f(n+4)+(690797/1083289334400)*h*f(n)+y[n+4]:
e6:=y[n+14/3] = -(29107/10333575)*h*f(n+5)+(7757824/651015225)*h*f(n+9/2)+(180667/429975)*h*f(n+13/3)+(342733/2910600)*h*f(n+14/3)-(7253/795685275)*h*f(n+1)+(42467/578680200)*h*f(n+2)-(19853/31000725)*h*f(n+3)+(993749/8266860)*h*f(n+4)+(22037/33852791700)*h*f(n)+y[n+4]:
e7:=y[n+9/2] = -(115447/51609600)*h*f(n+5)-(21389/198450)*h*f(n+9/2)+(231041241/521830400)*h*f(n+13/3)+(43797591/883097600)*h*f(n+14/3)-(32833/3973939200)*h*f(n+1)+(48323/722534400)*h*f(n+2)-(91493/154828800)*h*f(n+3)+(1220071/10321920)*h*f(n+4)+(24863/42268262400)*h*f(n)+y[n+4]:
e8:=y[n+5] = (1989/22400)*h*f(n+5)-(61184/99225)*h*f(n+9/2)+(1496637/2038400)*h*f(n+13/3)+(2458917/3449600)*h*f(n+14/3)+(73/5174400)*h*f(n+1)-(31/313600)*h*f(n+2)+(359/604800)*h*f(n+3)+(1079/13440)*h*f(n+4)-(179/165110400)*h*f(n)+y[n+4]:



h:=0.01:
N:=solve(h*p = 8/8, p):
#N := 10:
#n:=0:
#exy:= [seq](eval(i+exp(-i)-1), i=h..N,h):
c:=1:
inx:=0:
iny:=0:

mx := proc(t,n):
   t + 0.01*n:
end proc:

exy := (x - 1.0 + exp(-x)):

vars := y[n+1],y[n+2],y[n+3],y[n+4],y[n+13/3],y[n+14/3],y[n+9/2],y[n+5]:

printf("%6s%20s%20s%20s\n", "h","numy1","Exact", "Error");
#for k from 1 to N/8 do
for c from 1 to N do

	par1:=x[n]=map(mx,(inx,0)),x[n+1]=map(mx,(inx,1)),
		x[n+2]=map(mx,(inx,2)),x[n+3]=map(mx,(inx,3)),
		x[n+4]=map(mx,(inx,4)),x[n+5]=map(mx,(inx,5)),
		x[n+13/3]=map(mx,(inx,13/3)),x[n+14/3]=map(mx,(inx,14/3)),
		x[n+9/2]=map(mx,(inx,9/2)):
	par2:=y[n]=iny:
	res:=eval(<vars>, fsolve(eval({e||(1..8)},[par1,par2]), {vars}));
	
	printf("%7.3f%22.10f%20.10f%17.3g\n", 
		h*c,res[8],(exy,[x=c*h]),abs(res[8]-eval(exy,[x=c*h]))):
		#c:=c+1:
	
	iny:=res[8]:
	inx:=map(mx,(inx,5)):
end do:

Dear all,

Please Kindly help to correct or modify the code above

Thank you and best regards
 

The rational expression at the beginning of the code is approximant. p1-p5 are conditions imposed on t, and are to be solved simultaneously to obtain a[0]-a[4] which are then substituted into t to obtain Cf. S1-S4 are to be obtained from Cf and its derivative.

However, I observed that Cf is not providing the desired results. What have I done wrong? Please Can someone be of help?

Thank you and kind regards

restart:
t:=sum(a[j]*x^j,j=0..2)/sum(a[j]*x^j,j=3..4):
F:=diff(t,x,x):
p1:=simplify(eval(t,x=q))=y[n]:
p2:=simplify(eval(t,x=q+h))=y[n+1]:
p3:=simplify(eval(F,x=q))=f[n]:
p4:=simplify(eval(F,x=q+h))=f[n+1]:
p5:=simplify(eval(F,x=q+2*h))=f[n+2]:
vars:= seq(a[i],i=0..4):
Cc:=eval(<vars>, solve({p||(1..5)}, {vars}));
for i from 1 to 5 do
	a[i-1]:=Cc[i]:
end do:
Cf:=t;
M:=diff(Cf,x):
s4:=y[n+2]=collect(simplify(eval(Cf,x=q+2*h)),[y[n],y[n+1],f[n],f[n+1],f[n+2]], recursive);
s3:=h*delta[n]=collect(h*simplify(eval(M,x=q)),{y[n],y[n+1],f[n],f[n+1],f[n+2]},factor);
s2:=h*delta[n+1]=collect(h*simplify(eval(M,x=q+h)),{y[n],y[n+1],f[n],f[n+1],f[n+2]},factor):
s1:=h*delta[n+1]=collect(h*simplify(eval(M,x=q+2*h)),{y[n],y[n+1],f[n],f[n+1],f[n+2]},factor):