RESUMEN

A difference method for the numerical integration of a nonlinear partial integrodifferential equation is considered. The integral term is treated by means of a convolution quadrature suggested by Lubich. Some results from Lubich’s discretized fractional calculus play a crucial role in proving consistency. The verification of stability and convergence is based on the nonnegative character of the real quadratic form associated with the convolution quadrature. A stability result is derived that is applicable to equations and numerical methods far more general than those treated in this paper.

RESUMEN

Surface-volume reactions occur in many physical systems such as biological and industrial processes. Though traditionally modeled as a surface, the reaction zone is usually a thin layer (often a gel) abutting a flowing fluid or gas. Therefore, one would expect a more realistic model for the reacting zone to include the effects of transport in the gel. In this paper we examine the BIAcore, a device for measuring rate constants which has this geometry. To explain anomalous measurements from the device, it has been proposed that some flow penetrates into the dextran (gel) layer, thus enhancing transport. To analyze the reversible kinetics, asymptotic and singular perturbation techniques are used, yielding linear and nonlinear integrodifferential equations. Explicit and asymptotic solutions are constructed for cases motivated by experimental design. The results indicate that such flow penetration effects are bound to be negligible in surface-volume reactions, regardless of the flow model used.