result (2) for a charged spherical particle and Hoskin's result A method is proposed to evaluate the accuracy of numerical (5) for two identically charged spherical particles. However, solutions of the nonlinear Poisson -Boltzmann equation for one cannot ensure that the new method is also of the same charged colloidal particles. It is derived from the principles of accuracy in more complex geometry as that in the compared electrostatic fields and is formulated as an integral equation. one. It is well known that there is a truncation error in each It is valid for arbitrary surface potential and complex geometry.
of these methods. The truncation error is different from one
Two examples are given: for a charged capillary and for a method to another due to the implemented procedure of the charged spherical particle. It is shown by the examples that the method. It is therefore important to have methods for asassessment method is reasonable. In addition, the first example sessing the accuracy of the numerical solutions when there indicates that the Debye -Huckel approximation is acceptable at wider ranges of r c and z than normally considered, if a rela-are not any previous results, neither analytical nor numerical, tive error ( ER ) of about 10% can be tolerated. The second to refer as comparison.
example suggests that the results of Loeb et al. of the electric
In particular, an objective accuracy assessment approach potentials ( 1961 ) should be interpolated linearly or nonlinearly is needed for general cases, which can be used to measure to achieve higher accuracy when they are used in further calcuthe accuracy not only of the numerical solution of a new lations. ᭧ 1998 Academic Press method, but also of the solution in a new geometry. In the