An approximate formalism is derived for solving problems in the one-velocity transport of neutrons in convex, isotropically scattering media. The integral transport equation is transformed to an equivalent infinite medium problem to which the synthetic kernel method may be applied. It is then shown that the neutron flux may be approximated by the solution of a set of coupled-diffusion type differential equations. These equations and their related boundary conditions are of the same form as the few-group diffusion equations so that solution may be obtained by use of existing multidimensional computer codes. Finally, the new formalism is applied to a number of simplified, though realistic, problems and the results are compared with corresponding results provided either by rigorous treatment or by other approximate theories. In general, the accuracy of the formalism and the computational effort required are comparable with the simplified spherical harmonics method. In addition, the flexibility available in choosing the parameters of the synthetic kernel offers the possibility of tailoring kernels to specific design problems.