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Phương pháp toán tử cho các phương trình vi phân và sai phân telegraph
Tóm tắt
Bài toán Cauchy cho các phương trình telegraph trừu tượng ${\frac{d^{2}u(t)}{dt^{2}}}+\alpha{\frac{du(t)}{dt}}+Au(t)+\beta u(t)= f(t)$ với điều kiện biên $0\leq t\leq T$, $u(0)=\varphi$, $u^{\prime}(0)=\psi$ trong không gian Hilbert H với toán tử tự liên hợp xác định dương A đã được nghiên cứu. Các ước lượng ổn định cho nghiệm của bài toán này đã được thiết lập. Các sơ đồ sai khác bậc nhất và bậc hai cho nghiệm xấp xỉ của bài toán này đã được trình bày. Các ước lượng ổn định cho nghiệm của các sơ đồ sai khác này cũng đã được thiết lập. Trong các ứng dụng, hai bài toán hỗn hợp cho các phương trình vi phân riêng phần telegraph đã được khảo sát. Các phương pháp đã được minh họa bằng các ví dụ số.
Từ khóa
#phương trình telegraph #bài toán Cauchy #ổn định #không gian Hilbert #sơ đồ sai khácTài liệu tham khảo
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