کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5776677 1632154 2017 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A meshless scheme for Hamiltonian partial differential equations with conservation properties
ترجمه فارسی عنوان
یک طرح مخرب برای معادلات دیفرانسیل جزئی همیلتون با خواص حفاظتی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات محاسباتی
چکیده انگلیسی
Based on quasi-interpolation, the paper proposes a meshless scheme for Hamiltonian PDEs with conservation properties. There are two key features of the proposed scheme. First, it is constructed from scattered sampling data. Second, it conserves energy for both linear and nonlinear Hamiltonian PDEs. Moreover, if the considered Hamiltonian PDEs additionally possess some other quadric invariants (i.e., the mass in the Schrödinger equation), then it can even preserve them. Error estimates (including the truncation error and the global error) of the scheme are also derived in the paper. To demonstrate the efficiency and superiority of the scheme, some numerical examples are provided at the end of the paper. Both theoretical and numerical results demonstrate that the scheme is simple, easy to compute, efficient and stable. More importantly, the scheme conserves the discrete energy and thus captures the long-time dynamics of Hamiltonian systems.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 119, September 2017, Pages 115-125
نویسندگان
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