Algorithms for Linear Differential Equations and Algebraic Functions.

提案#0098034范Hoeij，马克佛罗里达州立大学这个奖项将设计新的方法来解决线性微分方程和代数函数的集成，包括实现。 其意义在于微分方程被用于物理学、工程学、数学和许多其他科学。一些计算机代数软件有求解器，可以应用各种方法来搜索微分方程的封闭形式解。这个项目将导致新的方法，使更多的方程可以解决。实现也将被编写并通过网络分发，以便使用计算机求解微分方程的研究人员可以轻松地从结果中受益。求解非线性微分方程的算法将间接受益，因为此类算法通常将问题简化为线性微分方程。该奖项的第二个主题是提高代数函数积分算法的性能。这是必要的，因为现有的方法不足以有效地处理大的输入。

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.