【摘要】 给出了求解热方程边界值决定反问题的直接差分法和配置法两种数值算法。直接差分法采用Euler向后差分格式;配置法把反问题化为拟解问题,利用Lagrange插值基函数构造有限维逼近,从而将问题转化为求解一个代数方程组,最后采用正则化方法求解。数值结果表明:直接差分法的反演结果在区间的左端有较强的振荡,而配置法能够整体恢复左边界值,并且配置法可灵活选择正问题的数值格式获得较高的精度。更多还原

【Abstract】 In this paper,a direct difference method and a collocation method are applied to solve an inverse problem of boundary value determination of heat equation.The direct difference method adopts the Euler backward difference scheme.The collocation method first formulates the inverse problem to a quasisolution problem and then uses base function of Lagrange interpolation to construct finite dimension approximation.In this way,the original problem is turned into solution of a system of algebraic equations.Finally,regularization method is used to solve.Numerical result shows that the inversion result of direct difference method presents strong fluctuation at the left end of interval,while the collocation method can recover the left boundary value on the whole and is easy to obtain higher precision by choosing appropriate numerical format of the direct problem.更多还原