Hướng tới các ước lượng sai số cho các phân discret hóa không-thời gian tổng quát của phương trình truyền

Springer Science and Business Media LLC - Tập 23 - Trang 1-14 - 2020
Martin J. Gander1, Thibaut Lunet1
1Section de Mathématiques, University of Geneva, Genéve 4, Switzerland

Tóm tắt

Chúng tôi phát triển các ước lượng sai số mới cho phương trình truyền một chiều, xem xét các sơ đồ phân discret hóa không-thời gian tổng quát dựa trên phương pháp Runge-Kutta và các phân discret hóa sai phân hữu hạn. Sau đó, chúng tôi đưa ra các điều kiện về số điểm trên mỗi bước sóng cho một sai số cho phép nhất định từ những ước lượng mới này. Phân tích của chúng tôi cũng cho thấy sự tồn tại của các phương pháp phân discret hóa không-thời gian hợp lực cho phép đạt được một bậc độ chính xác hơn tại một số CFL nhất định. Các ước lượng sai số mới của chúng tôi có thể được sử dụng để phân tích sự lựa chọn các phân discret hóa không-thời gian được xem xét khi thử nghiệm các phương pháp song song theo thời gian.

Từ khóa

#phương trình truyền #ước lượng sai số #phân discret hóa không-thời gian #phương pháp Runge-Kutta #sai phân hữu hạn

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