两个新的减肥差分方程模型和解法

Two New Difference Equation Models of Weight Loss and Solutions

根据能量守恒和热量变化规律,建立了跑步减重的两个新的差分方程模型.首先,引入计算基础代谢的Liu公式,对基本模型做进一步的细化,得到一个改进的一阶线性差分方程模型;然后,基于BMI指数与跑步速度关系建立了另一个改进的一阶非线性差分方程模型,对两个改进的模型进行稳定性分析,得到模型存在稳定解的条件,并进行了解析和数值的求解计算;最后,分析了运动时间、热量消耗对体重变化的影响,结果表明改进后的模型更贴合实际情况.

According to the law of energy conservation and thermal variation build two new difference equation models for running weight loss.First,the Liu formula of calculating basal metabolism is drawn into the basic model which makes the model more specific and deducing an improved first-order linear difference equation model.Then,based on the relevance between BMI index and the velocity of running to build another improved first-order non-linear difference equation model.Gaining the conditions of stationary solutions for existence by analyzing the stability for those models,meanwhile,calculating the analytical and numerical solutions of models.After analyzing the relevant variable′s effection in weight change,such as movement time in jogging,calorie consumption of body and calorie intakes,the conclusions of that analysis suggest the improved model are more suitable to the reality than initial model.