6 edited body edited May 2 '18 at 18:10 121 5044 bronze badges How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax.? κ=0.2; xmax=10; eq1={1/κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3}; eq2={a''[x] == a[x] f[x]^2}; boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};  An attempt to use NDSolve with the shooting method didn't work. How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax. κ=0.2; xmax=10; eq1={1/κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3}; eq2={a''[x] == a[x] f[x]^2}; boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};  An attempt to use NDSolve with the shooting method didn't work. How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax? κ=0.2; xmax=10; eq1={1/κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3}; eq2={a''[x] == a[x] f[x]^2}; boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};  An attempt to use NDSolve with the shooting method didn't work. 5 improved format edited May 2 '18 at 17:58 bbgodfrey 45.7k1010 gold badges6363 silver badges114114 bronze badges How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax. \[Kappa]=0κ=0.2; xmax=10; eq1={1/\[Kappa]^2κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3}; eq2={a''[x] == a[x] f[x]^2}; boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};  An attempt to use NDSolve with the shooting method didn't work. How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax. \[Kappa]=0.2; xmax=10; eq1={1/\[Kappa]^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3}; eq2={a''[x] == a[x] f[x]^2}; boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};  An attempt to use NDSolve with the shooting method didn't work. How can one solve a coupled equation for f[x] and a[x] with known boundary conditions for f[x] and a'[x] at some -xmax and xmax. κ=0.2; xmax=10; eq1={1/κ^2 f''[x] == (a[x]^2 - 1) f[x] + f[x]^3}; eq2={a''[x] == a[x] f[x]^2}; boundaryconditions={f[-xmax] == 0, f[xmax] == 1, a'[-xmax] == 1/Sqrt[2], a'[xmax] == 0};  An attempt to use NDSolve with the shooting method didn't work. 4 edited tags | link edited May 2 '18 at 13:03 bbgodfrey 45.7k1010 gold badges6363 silver badges114114 bronze badges 3 deleted 40 characters in body edited May 1 '18 at 17:42 121 5044 bronze badges 2 added 1 character in body edited May 1 '18 at 13:36 121 5044 bronze badges 1 asked May 1 '18 at 12:06 121 5044 bronze badges