A numerical solver for rate equations and photon transport equations in nonlinear laser spectroscopy Original Research Article

A software package, named PRES, is presented for the numerical solution of the coupled system of rate equations and photon transport equation(s) which is useful in nonlinear UV/VIS/NIR laser spectroscopy investigating multiphoton processes of excitation and deactivation in the manifold of electronic excited states. By semidiscretization the system of partial differential equations is transformed into two systems of ordinary differential equations. Because rate equations are often stiff and nonlinear they are solved with a modification of the A-stable trapezoidal rule. For the solution of the photon transport equations a special Runge–Kutta method is developed.