一种求解变系数渗压固结微分方程的数值方法

对变系数渗压固结微分方程的求解过程进行了深入研究,提出一种精细积分半解析数值方法,首先对渗压固结微分方程在空间离散,建立起对于时间的常微分方程组,然后对时程积分,利用矩阵指数函数可以在计算机字长范围内精确计算的特点,得到精密解答.当指数函数用Taylor展开式的一阶近似替代时,精细积分转化为差分方程.用matlab语言编写程序进行求解,得到孔隙比在固结过程中的分布规律,并通过模型试验进行了验证.

A Numerical Method to Solve the Permeation Pressure Consol idation Differential Equation with Variable Coefficients

Based on the thorough research on the solution process of permeation pressure consolidation differential equation with variable coefficients,a semi-analytic numerical method with precise integration was educed.Firstly,the permeation pressure consolidation differential equation was dispersed in space and ordinary differential equations about time were founded.And then ordinary differential equations was integrated in time process.The precise conclusions were obtained utilizing the feature of matrix exponential function that could be calculated precisely within the limit of machine word length.When the exponential function was substituted approximately with the first term of Taylor expansion in serise,the precise integration would transform into difference equation.The equation was solved by the program of Matlab and the distribution law of void ratio during the consolidation process was obtained.Which were verified by model test.