Stiff Oscillatory Systems, Delta Jumps and White Noise
Stiff Oscillatory Systems, Delta Jumps and White Noise
复制标题
刚性振荡系统、Delta 跳跃和白噪声
DOI：
10.1007/s10208001002
复制
发表时间：
2013
影响因子：
3
通讯作者：
Cano B
中科院分区：
文献类型：
--
作者：
Cano B
介绍了刚性振荡系统的两个模型问题。两者都包含谐波振荡器的线性叠加，用作标量 ODE 的强制项。在第一种情况下，选择初始条件以使强迫项近似于δ函数，而在第二种情况下，则使其近似于白噪声。在这两种情况下，振荡器的最快固有频率是 OM(N)。模型问题在时间步长满足的刚性状态中进行数值积分。在这种情况下，在极限 N→ ∞ 和 Δt→ 0 的情况下研究算法的收敛性。对于白噪声问题，同时考虑强收敛性和弱收敛性。阶数减少现象通过数值观察并在理论上得到证明。
Two model problems for stiff oscillatory systems are introduced. Both comprise a linear superposition ofharmonic oscillators used as a forcing term for a scalar ODE. In the first case the initial conditions are chosen so that the forcing term approximates a delta function asand in the second case so that it approximates white noise. In both cases the fastest natural frequency of the oscillators isOM(N).The model problems are integrated numerically in the stiff regime where the time-stepsatisfiesThe convergence of the algorithms is studied in this case in the limitN→ ∞ and Δt→ 0.For the white noise problem both strong and weak convergence are considered. Order reduction phenomena are observed numerically and proved theoretically.