论文标题
Ginacde：与C ++库的高性能F-扩展和第一个积分方法用于求解非线性微分方程
GiNaCDE: the high-performance F-expansion and First Integral Methods with C++ library for solving Nonlinear Differential Equations
论文作者
论文摘要
我们介绍了三种流行方法的算法：F-扩展，修改的F型扩展和第一种积分方法，以自动获得非线性偏微分方程（NLPDES）的封闭形式的行进波解决方案。我们概括并改善方法。所提出的算法是可管理的，直接且功能强大的工具，可对非线性普通微分方程（NLODES）和NLPDE的精确解决方案进行高性能评估。对于具有参数的微分方程，新算法确定参数的条件以获得精确的解决方案。该算法显示了各种Nlodes和NLPDE的解决方案，无论是可集成还是不可集成的。它可以求解包含复杂函数的Nlodes和NLPDE。该算法在名为Ginacde的C ++库中实现。在Ginacde的帮助下，一些示例证明了算法的效率和有效性。输出结果与先前已知的结果相结合，在某些情况下，明确获得了新的精确旅行波解决方案。解决了库的使用，实施问题，范围，限制和未来的软件扩展。
We present the algorithms for three popular methods: F-expansion, modified F-expansion, and first integral methods to automatically get closed-form traveling-wave solutions of nonlinear partial differential equations (NLPDEs). We generalize and improve the methods. The proposed algorithms are manageable, straightforward, and powerful tools providing a high-performance evaluation of the exact solutions of nonlinear ordinary differential equations (NLODEs) and NLPDEs. For differential equations with parameters, the new algorithms determine the conditions on the parameters to obtain exact solutions. The algorithms show solutions to a wide variety of NLODEs and NLPDEs, both integrable and non-integrable. It can solve NLODEs and NLPDEs that contain complex functions. The algorithms are implemented in a C++ library named GiNaCDE. The efficiency and effectiveness of the algorithms are demonstrated by some examples with the help of GiNaCDE. The output results tally with the previously known results, and in some cases, new exact traveling-wave solutions are explicitly obtained. Use of the library, implementation issues, scope, limitations, and future extensions of the software are addressed.
