(* Install BVPh 1.0 for Mathematica 5.2. *) (* For Mathematica 8.0, please replace BVPh1_0.txt by BVPh1_1.txt *) < BVP in a finite domain [0,a] *) (* TypeEQ = 2 -> eigenvalue problem in a finite domain [0,a] *) (* TypeL = 1 -> Chebyshev polynomial as base function *) (* TypeL = 2 -> Hybrid-base approximation *) (* TypeBase = 1 -> sine + polynomial *) (* TypeBase = 2 -> cosine + polynomial *) (* ApproxQ = 0 -> do NOT approximate the function *) (* Appprox = 1 -> approximate the function *) (************************************************************************) TypeEQ = 1; TypeL = 1; TypeBase = 2; ApproxQ = 0; NgetErr = 1; (************************************************************************) (* Define the governing equation *) (************************************************************************) f[z_,u_,lambda_] := D[u,{z,4}] + alpha*(z*D[u,{z,3}] + 3*D[u,{z,2}]) + R( u*D[u,{z,3}] - D[u,z]*D[u,{z,2}] ); alpha = 3/2; R = -11; (***********************************************************************) (* Define Boundary conditions *) (***********************************************************************) zR = 1; OrderEQ = 4; BC[1,z_,u_,lambda_] := Limit[u, z->0] ; BC[2,z_,u_,lambda_] := Limit[D[u,{z,2}], z->0 ]; BC[3,z_,u_,lambda_] := u - 1 /. z->zR; BC[4,z_,u_,lambda_] := D[u,z] /. z->zR; (************************************************************************) (* Define initial guess *) (************************************************************************) u[0] = sigma*z +(5-4*sigma)/2*z^3-(3-2*sigma)/2*z^5; sigma = .; (************************************************************************) (* Define output term *) (************************************************************************) output[z_,u_,k_]:= Print["output = ",D[u[k],z]/.z->0//N]; (************************************************************************) (* Defines the auxiliary linear operator *) (************************************************************************) omega[1] = Pi/zR; omega[2] = Pi/zR; L[f_] := Module[{temp,numA,numB,i}, If[TypeL == 1, temp[1] = D[f,{z,OrderEQ}], numA = IntegerPart[OrderEQ/2]; numB = OrderEQ - 2* numA//Expand; temp[0] = D[f,{z,numB}]; For[i=1, i<=numA, i++, temp[1] = D[temp[0],{z,2}] + (kappa*omega[i])^2*temp[0]; temp[0] = temp[1]; ]; ]; temp[1]//Expand ]; (* Print input and control parameters *) PrintInput[u[z]]; (* Set c0 and sigma *) c0 =-1/2; sigma = 2; Print[" c0 = ",c0, " sigma = ",sigma]; (* Gain HAM approximations by the 3rd-order iteration approach *) iter[1,40,3];