Algorithms for Linear Differential Equations and Algebraic Functions.

提案#0098034美国佛罗里达州立大学范霍伊该奖项将设计出解线性微分方程式和积分代数函数的新方法，包括实现。重要的是，微分方程式在物理、工程、数学和许多其他科学中都有应用。几个计算机代数软件都有解算器，它们应用不同的方法来搜索微分方程的闭合形式解。这个项目将带来新的方法，这样就可以解更多的方程。实现也将被编写并通过网络分发，这样使用计算机求解微分方程的研究人员就可以很容易地从结果中受益。求解非线性微分方程组的算法将间接受益，因为此类算法通常将问题归结为线性微分方程组。该奖项的第二个主题是改进代数函数积分算法的性能。这是必要的，因为现有方法的效率不足以处理大量输入。

Proposal #0098034Van Hoeij, MarkFlorida State UniversityThis award will devise new methods for solving linear differential equations and for integration of algebraic functions, including implementations. The significance is that differential equations are used in physics, engineering, mathematics and many other sciences. Several computer algebra softwares have solvers that apply various methods to search for closed-form solutions of differential equations. This project will lead to new methods, so that more equations can be solved. Implementations will be written as well and distributed via the web so that researchers who use a computer to solve differential equations can easily benefit from the results. Algorithms for solving non-linear differential equations will benefit indirectly because such algorithms often reduce problems to linear differential equations. The second topic in this award consists of improving the performance of the algorithm for integration of algebraic functions. This is necessary because the the existing method is not efficient enough to handle large inputs.