## finite difference, used finite difference for mkdv equation but error error how reformer

SetOptions[ListPlot,ImageSize->300,PlotRange->{All,All},Joined->True]; {n = 800, m = 100, a = 0,[CapitalTheta]= 0.5[Mu]= 1,[Epsilon]= 3, b = 80, tF = 1, h = (b-a) / n // N, k = tF / m // N, r1 = ([Epsilon] k) / (2 h), r2 = ([Mu] k) / (2 h ^ 3)}
F[x_]: = Sqrt[(6*0.3)/3] sech[Sqrt[0.3/1] (X)]// NOT;
Table[xN[i]= a + ih, {i, 0, n}];
ic = table[uN[i,0]-> f[xN[i]], {i, 0, n}];`Finite difference`
bc = {Table[uN[i,j]-> 0, {i, 0, n}]};
ibc = flatten[{ic,bc}];
fd[i_,j_]: = UN[i,j+1]-UN[i,j]+ r1
(UN[i,j]^ 2)([CapitalTheta] (UN[i+1,j+1]-UN[i-1,j+1]) + (1-[CapitalTheta])(UN[i+1,j]-UN[i-1,j])) + r2 * ([CapitalTheta]*(UN[i+2,j+1]-2 * uN[i+1,j+1]+ 2 * ONE[i-1,j+1]-UN[i-2,j+1]) + (1-[CapitalTheta])*(UN[i+2,j]-2 united[i+1,j]+ 2 * ONE[i-1,j]-UN[i-2,j]));
Make[{Do[{uN[-2,j]= UN[2,j],UN[-1,j]= UN[1,j],UN[n+2,j]= UN[n-2,j],UN[n+1,j]= UN[n-1,j]}, {i, 0, n}]}, {j, 0, m + 1}

;
Make[UN[a[ONU[uN[i,j+1]= fd[i,j]/.ibc,{j,0,m},{i,1,n-1}]; {l1 = {0,5,10}, nl1 = Length[l1]}
Make[g[j]= ListPlot[Table[{xN[i],UN[i,l1[[j]]]/.ibc},{i,0,n}], AxesLabel -> {"X", "U"}], {j, 1, nl1}];
Show[Table[g[i], {i, 1, nl1}], Frame-> True, Axes-> True]