I need to solve three coupled differential equations. The equations are as follows: dE1/dz = f(E2,E3) dE2/dz = f(E1,E3) dE3/dz = f(E1,E2) Where E1,E2,E3 represents field amplitudes. In case of plane waves these amplitudes will be constant in the transverse direction therefore i can directly solve these equation given their initial values. Although, i would like to, how should i solve these equations if i have a Gaussian distribution in the transverse direction? Do i need to solve it by creating a mesh and solving these equations for each pairs of points? I thank you for your time.