(* 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 = 2; TypeL = 1; TypeBase = 2; ApproxQ = 0; Ntruncated = 20; (************************************************************************) (* Define the governing equation *) (************************************************************************) f[z_,u_,lambda_] := lambda*D[u,{z,4}]-beta*z-beta*z*u^2*lambda^2; beta = 10 ; (***********************************************************************) (* Define Boundary conditions *) (***********************************************************************) zR = 1; OrderEQ = 4; BC[0,z_,u_,lambda_] := u - 1 /. z -> 1 ; BC[1,z_,u_,lambda_] := Limit[u, z -> 0 ]; BC[2,z_,u_,lambda_] := D[u,z] /. z -> 1 ; BC[3,z_,u_,lambda_] := D[u,{z,2}] /. z -> 1; BC[4,z_,u_,lambda_] := Module[{temp}, temp[1] = D[u,{z,2}] /. z -> 0; temp[2] = D[u,{z,2}] /. z -> alpha; temp[1]-temp[2]//Expand ]; alpha = 1/5; (************************************************************************) (* Define initial guess *) (************************************************************************) u[0] = sigma/(2*alpha-3)*((6*alpha-8)*z+6*(1-alpha)*z^2+2*alpha*z^3-z^4); sigma = 1; (************************************************************************) (* 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]]; (* Use 3rd-order HAM iteration *) iter[1,6,3];