# Question:how to plot different values of Mh

## Question:how to plot different values of Mh

Maple 18

How to get a plot for different values of Mh.

like Mh=[1 2 3 4]

Code:

restart;

m:=10;H:=1;Mh:=1;b:=0.02; a:=0.05;V:=array(0..m); V[0]:=1-exp(-t);

for k from 1 to m do

if k=1 then chi:=0;

chi:=1;

fi;

p:=0;

for j from 0 to k-1 do

p:=p+(V[k-1-j]*diff(V[j],t\$2)-diff(V[k-1-j],t)*diff(V[j],t)-a*(2*diff(V[k-1-j],t)*diff(V[j],t\$3)-diff(V[k-1-j],t\$2)*diff(V[j],t\$2)-V[k-1-j]*diff(V[j],t\$4)));  od;

p:=(p+diff(V[k-1],t\$3)-b*(diff(V[k-1],t\$2)+t*diff(V[k-1],t\$3))-Mh*diff(V[k-1],t))*h*H;

p:=factor(p);

V[k]:=(-int(p,t)+0.5*exp(t)*int(exp(-t)*p,t)+0.5*exp(-t)*int(exp(t)*p,t)+chi*V[k-1]+C1+C3*exp(-t));

v:=unapply(V[k],t);

V[k]:=frontend(expand,[V[k]]);  V[k]:=subs(C3=solve(eval(subs(t=0,diff(V[k],t))),C3),V[k]); V[k]:=frontend(expand,[V[k]]);

V[k]:=subs(C1=solve(eval(subs(t=0,-V[k]-diff(V[k],t))),C1),V[k]);

od:

appr:=0;

for k from 0 to m do

appr:=appr+V[k];

od:

u_appr:=unapply(appr,(h,t)):

u_appr_1:=unapply(diff(u_appr(h,t),t),(h,t)):

evalf(u_appr_1(-0.4,t)):

with(plots);

plot([u_appr_1(-0.4,t)],t=0..4,0..1.2,color=[black],axes=frame):

this plot for Mh=1:

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