I am trying to solve differential equations by using Homotopy analysis method code but am unable, Please, somebody guide me to success. I am new to this forum.
In[358]:= (*Clear all variables*)ClearAll["Global`*"];
(*Load the required packages*)
Get["C:\\BVPh2\\Package\\BVPh2_0.m"];
Get["C:\\Users\\HP\\Documents\\MATHEMATICA program\\HAM11.m"];
(*Define the type and number of equations*)
TypeEQ = 1;
NumEQ = 2;
(*Define the functions and equations*)
f[1, z_, {f_, g_}, Lambda_] := (1 + K) D[f, {z, 4}] -
Rey M D[f, {z, 2}] + 2 Rey f D[f, {z, 3}] - K D[g, {z, 2}];
f[2, z_, {f_, g_}, Lambda_] := (1 + K/2) D[g, {z, 2}] -
Rey K (2 g - D[f, {z, 2}]) + Rey (2 f D[g, z] - D[f, z] g);
(*Define the boundary conditions*)
NumBC = 6;
BC[1, z_, {f_, g_}] := f /. z -> 0;
BC[2, z_, {f_, g_}] := f /. z -> 1;
BC[3, z_, {f_, g_}] := (D[f, z] - 1) /. z -> 1;
BC[4, z_, {f_, g_}] := D[f, {z, 2}] /. z -> 0;
BC[5, z_, {f_, g_}] := g /. z -> 1;
BC[6, z_, {f_, g_}] := g /. z -> 0;
(*Define the initial guesses and linear operators*)
zL[1] = 0; zR[1] = 1;
zL[2] = 0; zR[2] = 1;
U[1, 0] = (z^3 - z)/2;
U[2, 0] = 0;
L[1, u_] := D[u, {z, 4}];
L[2, u_] := D[u, {z, 2}];
(*Set parameters and solve*)
Rey = M = 2;
K = 1/2;
GetOptiVar[4, {}, {c0[1], c0[2]}];
BVPh[1, 20];
(*Plot the results*)
Plot[{U[1, 20], U[2, 20]}, {z, 0, 1}, AxesLabel -> {"z", ""},
PlotStyle -> {{Thin, Red}, {Dashed, Blue}},
PlotRange -> {{0, 1}, {-0.2, 0.2}}]
ListLogPlot[Table[{2 i, ErrTotal[2*i]}, {i, 1, 10}], Joined -> True,
Mesh -> All, PlotRange -> {{2, 20}, {10^(-34), 1}},
AxesLabel -> {"m", "error"}]
%% ERROR:
During evaluation of In[358]:= Get::noopen: Cannot open C:\BVPh2\Package\BVPh2_0.m.
During evaluation of In[358]:= Get::noopen: Cannot open C:\Users\HP\Documents\MATHEMATICA program\HAM11.m.
Out[382]= \!\(\*
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Out[383]= \!\(\*
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