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Approximate method for nonlinear differential and integrodifferential equations



A generalized variable-parameter averaging (GVPA) method to solve nonlinear differential and integrodifferential equations is formulated. The method uses a constant-parameter solution to the original problem together with averaging and interpolation to obtain approximate solutions to some chemical engineering problems with variable parameters, such as transfer coefficients or permeate velocity. The efficiency of the method is studied with application to the ultrafiltration in dead-end outside-in hollow-fiber modules, filtration in hollow-fiber membrane adsorbers, mass transfer with a variable diffusion coefficient, and concentration polarization in unstirred reverse osmosis batch cells. Comparison with the numerical solutions to the complex chemical engineering problems shows that the solutions obtained by the GVPA method provide a sufficient accuracy in describing the process performance and dramatically cut down the computation time. © 2006 American Institute of Chemical Engineers AIChE J, 2006