一类非线性边界条件的抛物型方程组的周期解的数值解法(英文)

NUMERICAL METHODS FOR PERIODIC SOLUTIONS OF PARABOLIC SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS

本文研究了一类具有非线性边界条件的反应扩散对流方程组的周期解的数值解法,利用上下解作为初始迭代,把求方程组的Jacobi方法和Gauss Seidel方法和上下解方法结合起来,得到了迭代序列的单调收敛性和方法的收敛性,对方法的稳定性也作了论述。

This paper is devoted to numerical methods of periodic solutions for a class of nonlinear reaction-diffusion-convection systems under nonlinear boundary conditions. Combining the method of upper and lower solutions with Jacobi or Gauss-Seidel method, we can gain the monotone convergence of the iterative sequences and the convergence of the methods. The numerical stability of these schemes is also discussed.