Algorithms for Linear Differential Equations and Algebraic Functions.

点击翻译按钮获取中文摘要

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.