【摘要】 讨论了一类二阶抛物型方程反问题的数值解法。应用拟解法的思想,把原问题分解为一系列适定的正问题和一个不适定的线性代数方程组。对于相应的正问题,证明了解连续依赖于初始分布,由此得到了在时刻的稳定性估计。使用古典欧拉差分格式求解正问题和用截断奇异值分解法求解病态方程组。数值结果显示数值解与理论解吻合很好。更多还原

【Abstract】 A method of solution of backward second-order parabolic equation problem is discussed in the article.The method employs a quasisolution approach and is based on the separation of the problem into a sequence of well-posed forward problems and an ill-posed system of algebraic equations.For the corresponding forward problem the continuous dependence of the solution on the initial data is proved.From this result a stability estimate on the final time T is obtained.Using the perform of classic Euler solves the forward problem the ill-conditioned system of algebraic equation is solved by using truncated singular value decomposition.The result manifests that the numerical solution and theoretical solution are well consistent.更多还原