标题： 无振荡方法用于噪声初始条件下的半线性扩散方程 显示英文标题

标题： Oscillation-free method for semilinear diffusion equations under noisy initial conditions

摘要： 初始条件中的噪声来自测量误差，可能导致不希望的振荡，并在数值解中传播。我们提出了一种技术，在求解半线性扩散方程的初边值问题时防止这种振荡误差。对称Strang分裂被应用于方程，以分别求解线性扩散和非线性余项。开发了一种无振荡方案，以克服数值求解线性扩散部分时的任何振荡行为。为了展示稳定振荡的危害，我们将我们的方法与加权隐式欧拉方案与Crank-Nicolson方法进行比较。通过局部线性化分析了我们方法的无振荡特性和稳定性。我们的无振荡方法的准确性得到了证明，并通过求解一个Fisher型方程进一步验证了其有效性，在初始条件存在随机误差的情况下成功产生了无振荡解。 显示英文摘要

摘要： Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of semilinear diffusion equations. Symmetric Strang splitting is applied to the equation for solving the linear diffusion and nonlinear remainder separately. An oscillation-free scheme is developed for overcoming any oscillatory behavior when numerically solving the linear diffusion portion. To demonstrate the ills of stable oscillations, we compare our method using a weighted implicit Euler scheme to the Crank-Nicolson method. The oscillation-free feature and stability of our method are analyzed through a local linearization. The accuracy of our oscillation-free method is proved and its usefulness is further verified through solving a Fisher-type equation where oscillation-free solutions are successfully produced in spite of random errors in the initial conditions.