Rate of convergence of the method of lines for the nonlinear parabolic integrodifferential equation describing a photon recycling diode

We consider the Dirichlet problem and the mixed boundary-value problem for a nonlinear integro-differential equation of a parabolic type, which provides a mathematical model of the various modes in a photon-recycling semiconductor diode. The existence of the mixed derivative ²u/tx is proved for the solution of these problems. Method-of-lines schemes are constructed. An O(h) rate of convergence bound is established for the equation with nonlinear integral and differential components and an O(h²) bound for the equation with a nonlinear integral part.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 74, pp. 21–31, 1992;