rohitner/MA20102

In[47]:= ClearAll["Global`*"];
D1u[x_,u_,v_]=v;
D2u[x_,u_,v_]=2*u*v;
D3u[x_,u_,v_]=2*v^2+2*u^2*v;
D1v[x_,u_,v_]=2*u*v;
D2v[x_,u_,v_]=2*v^2+2*u^2*v;
D3v[x_,u_,v_]=8*u*v*2*v+u^2;
sn0=0.5;
sn1=0.1;
x0=0;
xf=1;
gamma=1;
n=4;
phin0=1;
phin1=1;
x=Table[j,{j,1,n+1}];
u1=Table[j,{j,1,n+1}];
v1=Table[j,{j,1,n+1}];
u2=Table[j,{j,1,n+1}];
v2=Table[j,{j,1,n+1}];
h=xf-x0  n;
u10=0.5;
u20=0.5;
Whilephin1>0.005,
v10=sn0;
x[[1]]=x0;
u1[[1]]=u10;
v1[[1]]=v10;
Fori=1,i<n+1,i++,
u1[[i+1]]=u1[[i]]+h*D1u[x[[i]],u1[[i]],v1[[i]]]+h^2  2*D2u[x[[i]],u1[[i]],v1[[i]]]+h^3  6*D3u[x[[i]],u1[[i]],v1[[i]]];
v1[[i+1]]=v1[[i]]+h*D1v[x[[i]],u1[[i]],v1[[i]]]+h^2  2*D2v[x[[i]],u1[[i]],v1[[i]]]+h^3  6*D3v[x[[i]],u1[[i]],v1[[i]]];
x[[i+1]]=x[[i]]+h;
;
datau1=Transpose[{x,u1}];
datav1=Transpose[{x,v1}];
v20=sn1;
x[[1]]=x0;
u2[[1]]=u20;
v2[[1]]=v20;
Fori=1,i<n+1,i++,
u2[[i+1]]=u2[[i]]+h*D1u[x[[i]],u2[[i]],v2[[i]]]+h^2  2*D2u[x[[i]],u2[[i]],v2[[i]]]+h^3  6*D3u[x[[i]],u2[[i]],v2[[i]]];
v2[[i+1]]=v2[[i]]+h*D1v[x[[i]],u2[[i]],v2[[i]]]+h^2  2*D2v[x[[i]],u2[[i]],v2[[i]]]+h^3  6*D3v[x[[i]],u2[[i]],v2[[i]]];
x[[i+1]]=x[[i]]+h;
;
datau2=Transpose[{x,u2}];
datav2=Transpose[{x,v2}];
phin0=Abs[u1[[n+1]]-gamma];
phin1=Abs[u2[[n+1]]-gamma];
sn2=sn1-sn1-sn0  phin1-phin0*phin1;
sn0=sn1;
sn1=sn2;

In[70]:= u1
Out[70]= {1,2,3,4,5}