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用积分算子方法求二阶数值微分 被引量:1
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作者 吕小红 吴传生 高飞 《武汉理工大学学报》 EI CAS CSCD 北大核心 2008年第6期178-180,共3页
数值微分就是用离散方法近似地求出函数在某点的导数值。关于数值微分己有许多求解方法,但这些方法都有各自的局限性,且关于二阶导数近似逼近的方法研究相对较少。基于Groetsch的思想,提出了利用积分算子来构造近似二阶导数的方法,并将... 数值微分就是用离散方法近似地求出函数在某点的导数值。关于数值微分己有许多求解方法,但这些方法都有各自的局限性,且关于二阶导数近似逼近的方法研究相对较少。基于Groetsch的思想,提出了利用积分算子来构造近似二阶导数的方法,并将此方法应用于二阶数值微分问题,给出了相应的误差估计。通过数值实验表明,此方法对于二阶数值微分问题十分有效,而且计算量小。 展开更多
关键词 二阶数值微分 积分算子 不适定问题 正则化
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对二阶数值微分算法的一些改进与对比试验研究
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作者 颜青 张华 《河北工业大学学报》 CAS 北大核心 2011年第4期51-55,59,共6页
基于Tikhonov正则化方法,对一种第一类Fredholm积分方程进行离散正则化处理,得到了求解一类带扰动离散数据二阶导数的稳定算法,它在数据的误差水平已知和未知情况下均可应用.基于Richardson外推算法对半离散正则化算法进行了改进.最后... 基于Tikhonov正则化方法,对一种第一类Fredholm积分方程进行离散正则化处理,得到了求解一类带扰动离散数据二阶导数的稳定算法,它在数据的误差水平已知和未知情况下均可应用.基于Richardson外推算法对半离散正则化算法进行了改进.最后设计了全面、系统的数值试验,对现行几种二阶数值微分算法的性能进行测试、比较和分析.实验数据的有关分析和结论对于算法在实际工程中的应用提供了有益的参考. 展开更多
关键词 二阶数值微分 算法 不适定性 正则化 第一类FREDHOLM积分方程
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Quantitative Evaluation of Neuroplastic Biomaterial for Human Brain Rehabilitation to Stroke Subjects
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作者 Chiyuri Nagayama 《Journal of Chemistry and Chemical Engineering》 2013年第11期1036-1043,共8页
Neurorehabilitation involves training of brain activity, which influences the resistive torque and electromyogram. This quantitative evaluation is numerical modeling of biomaterial of human body. Measurement for rehab... Neurorehabilitation involves training of brain activity, which influences the resistive torque and electromyogram. This quantitative evaluation is numerical modeling of biomaterial of human body. Measurement for rehabilitation and developing numerical modeling in patients are useful for information technology education with healthcare background. The resistive torque and electromyogram were measured. Electromyogram is the neuronal activity from eight lower limb muscles. Both activities are output signals for angle input signals. The resistive torque of a stroke patient shows a hysteresis curve, and this is a velocity-dependent component, particular for stroke. Differentiated angle by muscle spindle, a velocity-dependent component, is a stretch reflex (spasticity). In an electromyogram of a stroke patient, SLR (stretch reflex via spinal cord) means a short latency reflex, and LLR (stretch reflex via cerebral cortex) means a long latency reflex. An example of some stroke electromyogram shows long latency reflex, and this is voluntary movement during the experiment. The example of some stroke resistive torque reveals that viscoelasticity is used for the intrinsic component. The example of some stroke electromyogram reveals that long latency reflex is used for the reflex component of lower limbs. Current research needs improvement. Intrinsic viscoelasticity is modeled by a second-order differential equation. The reflex component of stroke patients is modeled by a double exponential function. Open source software is in use. Information technology-based analyses by numerical modeling would be applied in future healthcare education. 展开更多
关键词 Analysis programming biological tissue educational effect developmental process.
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