Nghiên cứu so sánh ba phương pháp số để giải phương trình tích phân vi phân kiểu Atangana–Baleanu được định nghĩa theo nghĩa Caputo

Engineering with Computers - Tập 38 - Trang 149-168 - 2020
Deeksha Singh1, Farheen Sultana1, Rajesh K. Pandey1, Abdon Atangana2,3
1Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi, India
2Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa
3Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Tóm tắt

Nghiên cứu này chứa các phương pháp số bao gồm phương pháp Tuyến tính, phương pháp Bậc hai và phương pháp Bậc hai-tuyến tính để giải một phương trình tích phân vi phân phân số sử dụng đạo hàm Atangana–Baleanu được định nghĩa theo nghĩa Caputo. Ranh giới sai số của các phương pháp được thu được. Chúng tôi thảo luận về bốn ví dụ thử nghiệm để thực hiện các mô phỏng số và kết quả số thu được đảm bảo rằng các phương pháp trình bày hoạt động tốt và nghiệm gần đúng thu được phù hợp với nghiệm phân tích. Độ hội tụ và sai số tuyệt đối cực đại của các phương pháp được tính toán và hiệu suất so sánh của chúng được thảo luận.

Từ khóa

#phương pháp số #phương trình tích phân vi phân #phân số #đạo hàm Atangana–Baleanu #nghĩa Caputo

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