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.