论文标题
周期性系列的开发，解决微分方程的方法
Development in periodic series,method for resolving differential equations
论文作者
论文摘要
在泰勒和弗罗贝尼乌斯系列中实际变量的功能的发展（整个系列中，在非正交的，非周期基础中形成），在正弦曲线级别（正交，周期性功能的基础）中，在一系列特殊功能中（正交，非周期性函数的基础），用于循环的差异等等。在本文中，基于对周期性正弦曲傅里叶序列（SFS）的性能的深入分析，我们将能够将此过程应用于更广泛的气体（所有线性，同质和非同性方程式），具有恒定型和非固定型的构造和非元素的类别，具有变量和非元素等式的变量范围，并具有变量的变量，并具有变量的变量。 integro-diffingential方程等）。我们还将扩展此过程，并使用它来解决以非正交周期性碱基的某些ODE，以非正弦曲线周期性傅立叶级数（SFN）表示。
The development of functions of real variables in Taylor and Frobenius series (whole series which are formed in nonorthogonal, nonperiodic bases), in sinusoidal Fourier series (bases of orthogonal, periodic functions), in series of special functions (bases of orthogonal, nonperiodic functions), etc. is a commonly used method for solving a wide range of ordinary differential equations (ODEs) and partial differential equations (PDEs).In this article, based on an in-depth analysis of the properties of periodic sinusoidal Fourier series (SFS), we will be able to apply this procedure to a much broader category of ODEs (all linear, homogeneous and non-homogeneous equations with constant coefficients, a large category of linear and non-linear equations with variable coefficients, systems of ODEs, integro-differential equations, etc.). We will also extend this procedure and we use it to solve certain ODEs, on non-orthogonal periodic bases, represented by non sinusoidal periodic Fourier series (SFN).
