论文标题
二阶偏微分方程的蓝调函数方法：应用于非线性电报方程
The BLUES function method for second-order partial differential equations: application to a nonlinear telegrapher equation
论文作者
论文摘要
研究了基于蓝色扩展（方程叠加的线性使用）函数方法的分析迭代序列到具有二阶时间导数的部分微分方程（PDE）。布鲁斯方法的原始公式是通过引入矩阵形式主义来修改的，该矩阵形式主义考虑了高阶时间导数的初始条件。现在，解决方案及其衍生物的初始条件都起着源向量的作用。该方法在非线性电报方程式上进行了测试，可以通过合适的参数选择将其简化为非线性波方程。此外，与其他三种方法进行了比较：Adomian分解方法，变分迭代方法（具有绿色函数）和同型扰动方法。对于其他方法，矩阵蓝调函数方法被证明是值得的替代方法。
An analytic iteration sequence based on the extension of the BLUES (Beyond Linear Use of Equation Superposition) function method to partial differential equations (PDEs) with second-order time derivatives is studied. The original formulation of the BLUES method is modified by introducing a matrix formalism that takes into account the initial conditions for higher-order time derivatives. The initial conditions of both the solution and its derivatives now play the role of a source vector. The method is tested on a nonlinear telegrapher equation, which can be reduced to a nonlinear wave equation by a suitable choice of parameters. In addition, a comparison is made with three other methods: the Adomian decomposition method, the variational iteration method (with Green function) and the homotopy perturbation method. The matrix BLUES function method is shown to be a worthwhile alternative for the other methods.
