Phương pháp cầu phương thích ứng xấp xỉ tích phân kép trên miền hình chữ nhật cong

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Tác giả: Văn Tiệp Đinh, Thị Thu Hằng Phạm

Ngôn ngữ: vie

Ký hiệu phân loại: 513.58 Arithmetic

Thông tin xuất bản: Khoa học và Công nghệ (Đại học Thái Nguyên), 2018

Mô tả vật lý: 179-183

Bộ sưu tập: Metadata

ID: 492113

Thêm vào giỏ

Recently, in an early publication, the author presented an algorithm to approximate double integral over a rectangle basing on the adaptive quadrature method. This method has the upper hand comparing with many other approaches due to its low cost and high efficiency. In that paper, even the algorithm was constructed strictly for approximating double integrals over rectangles only, it can be also extended to treat the case of non-rectangular regions. Nevertheless, for non-rectangular regions, it is not somewhat practical to program such an algorithm because of the consumption a large amount of RAM to store data of values for functions taking on the boundary of the region. The storage is performed at many steps in each repeating loop. This shortcoming often makes the program implement awkwardly. This paper aims to revise the aforementioned algorithm to be more efficient.Trình bày một thuật toán xấp xỉ tích phân kép trên miền hình chữ nhật dựa trên phương pháp cầu phương thích ứng. Phương pháp này tỏ ra vượt trội hơn các phương pháp cầu phương khác bởi chi phí thấp song hiệu quả cao. Mặc dù thuật toán chỉ được xây dựng cụ thể và chặt chẽ cho tích phân kép trên miền hình chữ nhật, nhưng nó có thể được mở rộng sang trường hợp của miền hình chữ nhật cong. Tuy nhiên, với miền hình chữ nhật cong, một chương trình được lập trình dựa trên thuật toán đó sẽ khá rườm rà bởi việc sử dụng một dung lượng lớn RAM máy tính để lưu trữ dữ liệu về giá trị hàm số trên biên của miền. Việc lưu trữ này được thực hiện trong nhiều bước tại mỗi vòng lặp. Điều này khiến chương trình thực thi chậm chạp, độ chính xác thấp.

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