A general, computational-mathematical modeling method for the solution of large, boundary-coupled transport problems involving the flow of mass, momentum, energy or subatomic particles is disclosed. The method employs a modeling processor that extracts a matrix operator equation (or set of equations) from a numerical transport code (NTC). The outputs of software codes, available for modeling physical problems governed by conservation laws in the form of differential equations, can be processed into closed-form operator equations with the method. Included is a numerical transport code functionalization (NTCF) model which can be determined numerically, based on a system of solutions of an NTC, evaluating outputs for a given set of inputs. The NTCF model is a linear or nonlinear, multi-variable operator equation or set of such equations. The NTCF model defines relationships between general, time-variable inputs and outputs, some known and some unknown, considered as boundary values. The user of an NTCF model can directly work with the processed model output, instead of running the original numerical code in general applications of a boundary-value problem. The numerical transport code functionalization model can be employed as a surrogate for representing the numerical transport code to provide a solution to the transport problem. The invention enables modeling efficiency and availability to be increased, while computational complexity and cost decreased. Computational times for complex modeling problems can, in some cases, be dramatically reduced, for example by several orders of magnitude.