一类非线性抛物方程的隐式解法及外迭代收敛性

Implicit Solution of Nonlinear Parabolic Equation and Convergence Nature of Outer Iteration Method

对一类非线性抛物方程进行研究,并针对该类方程建立了一种隐式差分格式.在此基础上,采用外迭代法及追赶法高效率地求解出该类方程的差分解,并利用VonNeumann条件证明了该差分格式的稳定性及外迭代法的收敛性,从而有效地解决了该类方程的数值计算问题 值得指出的是。

Nonlinear parabolic equations are widely used in practice. On most occasions only approximate solutions can be obtained by numerical calculations. A type of nonlinear parabolic equation is studied here.Implicit differential schemes are set up for this equation. Based on this, the differential schemes are solved by using outer iteration method and persuit method. The stability of the differential schemes is proved on Von Neumann's condition and the convergence nature of outer iteration method is analysed. Thus, the numerical problem of the equation is effectively solved. This method can be extended to the general nonlinear parabolic equation solutions. 