Numerical solution of Rothenberg's equation of the glottal airflow rate as a function of the glottal area using backward differentiation (L).

This letter shows the application of backward differentiation formulas to solve a differential equation by Rothenberg [(1981). Department for Speech, Music and Hearing Quarterly Progress and Status Report (KTH Royal Institute of Technology, Stockholm, Sweden), Vol. 22], which models the glottal airflow rate vs the glottal area. The formulas avoid a singularity of the equation that occurs when the glottal area is zero and that prevents the application of Runge-Kutta and other numerical methods. They can also be used when the equation is augmented with a glottal air viscosity term to eliminate non-differentiability at glottal opening and closure.