کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
401475 675366 2008 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Solving and factoring boundary problems for linear ordinary differential equations in differential algebras
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
Solving and factoring boundary problems for linear ordinary differential equations in differential algebras
چکیده انگلیسی

We present a new approach for expressing and solving boundary problems for linear ordinary differential equations in the language of differential algebras. Starting from an algebra with a derivation and integration operator, we construct an algebra of linear integro-differential operators that is expressive enough for specifying regular boundary problems with arbitrary Stieltjes boundary conditions as well as their solution operators.On the basis of these structures, we define a new multiplication on regular boundary problems in such a way that the resulting Green’s operator is the reverse composition of the constituent Green’s operators. We provide also a method for lifting any factorization of the underlying differential operator to the level of boundary problems. Since this method only needs the computation of initial value problems, it can be used as an effective alternative for computing Green’s operators in the case where one knows how to factor the given differential operators.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 43, Issue 8, August 2008, Pages 515-544