利用一阶和二阶导数的四阶padé型紧致差分逼近式,结合原方程本身,得到了两点边值问题的一种四阶精度的隐式紧致差分格式。该格式仅涉及未知量及其一阶导数和二阶导数值,推导过程简便。并且利用泰勒展开得到了一阶和二阶导数在边界点处的同阶离散格式。数值算例表明:文中格式较以往的格式具有更高的精度,并且计算简便。
Based on the padé schemes of first-and second-order derivatives,a fourth-order implicit compact difference scheme is proposed for solving two-point boundary value problem.Taylor expansions are used to construct the same order discretization of the boundary points.Numerical results prove the efficiency and dependability of present method.