Computational techniques are extensively applied in nonlinear science. However, while the use of computers for research has been expressive, the evaluation of numerical results does not grow in the same pace. Hammel et al. (Journal of Complexity, 1987, 3(2), 136--145) were pioneers in the numerical reliability field and have proved a theorem that a pseudo-orbit of a logistic map is shadowed by a true orbit within a distance of $10^{-8}$ for $10^{7}$ iterates. But the simulation of the logistic map with less than 100 iterates presents an error greater than $10^{-8}$ in a modern computer, performing a test based on the concept of multiple pseudo-orbits and symbolic computing.
翻译:计算技术在非线性科学中广泛应用,然而,虽然计算机用于研究的使用表现良好,但对数字结果的评价并没有以同样的速度增长,Hammel等人(《复杂程度杂志》,1987年,3(2)、136-145)是数字可靠性领域的先驱者,并证明一个理论是,后勤图的假轨道在10 ⁇ 8}美元以10 ⁇ 7}美元为代数的距离内的真实轨道上被一个假轨道所笼罩,但以不到100公升的代数模拟后勤图在现代计算机中出错大于10 ⁇ 8美元,进行基于多个伪轨道和象征性计算概念的测试。