| Abstract: | The nonlinear Poisson problems are very common in heat
conduction and diffusion with simultaneous reaction in a porous catalyst
particle, so the generalized quasilinearization theory is exploited and a
new numerical iterative method is proposed for this type nonlinear Poisson
problem. In this method, the nonlinear equation is replaced by a set of
iterative linear equation. An advantage of this method is that a theory
background is substantial for the choice of the initial value of the
iteration, and with a wide range of initial value the result of this
iteration is monotonously converged to the exact value. This new iterative
method is combined with boundary element method and dual reciprocity hybrid
boundary node method for solving nonlinear Poisson problems, and the
accuracy, the convergence rate and stability with different initial values
of these two methods are compared with each other. It is shown that, the
method based on dual reciprocity hybrid boundary node method and generalized
quasilinearization theory, has the high stability and efficiency, and the
iterative rate is quadratic. |
