论文标题
蓝色迭代应用于非线性普通微分方程进行波传播和传热
BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer
论文作者
论文摘要
基于蓝色（超出方程式叠加的线性使用）函数方法来计算与源非线性普通微分方程解的分析近似值的函数方法。研究了物理学的各种问题，并发现了近似分析解决方案。我们首先处理阻尼驱动的非线性振荡器，并表明该方法可以正确繁殖振荡行为。接下来，处理了一个用Stefan-Boltzmann冷却的半无限杆中描述热传递的分数微分方程。在这种情况下，与Adomian分解方法进行了详细的比较，其结果有利于Blues方法。作为最后的问题，涉及人口生物学的Fisher方程。在所有情况下，都表明解决方案在全球范围内或对于Fisher问题上局部或在局部问题上呈指数快速的固定溶液。
The iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method for calculating analytic approximants to solutions of nonlinear ordinary differential equations with sources is elaborated upon. Diverse problems in physics are studied and approximate analytic solutions are found. We first treat a damped driven nonlinear oscillator and show that the method can correctly reproduce oscillatory behaviour. Next, a fractional differential equation describing heat transfer in a semi-infinite rod with Stefan-Boltzmann cooling is handled. In this case, a detailed comparison is made with the Adomian decomposition method, the outcome of which is favourable for the BLUES method. As a final problem, the Fisher equation from population biology is dealt with. For all cases, it is shown that the solutions converge exponentially fast to the numerically exact solution, either globally or, for the Fisher problem, locally.
