یک روش جدید دوگامی متقارن ابرشکف P-پایدار از مرتبه جبری دوازدهم برای حل عددی مسائل مقدار اولیه مرتبه دوم
محورهای موضوعی : آمار
علی شکری
1
(
گروه ریاضی ، داشکده علوم پایه، دانشگاه مراغه، مراغه، ایران
)
عباسعلی شکری
2
(
عضو هیات علمی دانشگاه آزاد اسلامی واحد اهر
)
محمد مهدیزاده خالسرایی
3
(
گروه ریاضی، دانشکده علوم پایه، دانشگاه مراغه، مراغه، ایران
)
فیروز پاشائی
4
(
گروه ریاضی، دانشکده علوم پایه، دانشگاه مراغه، مراغه، ایران
)
کلید واژه: Moltiderivative methods, Stability region, Phase-lag, Initial value problems,
چکیده مقاله :
در این مقاله، یک روش جدید دوگامی خطی ابرشکف ضمنی از مرتبه جبری دوازدهم با استفاده از تکنیک صفر کردن فازتاخیری ومشتق های مراتب اول، دوم و سوم آن تولید و مورد تجزیه و تحلیل قرار می گیرد. هدف اصلی این مقاله، تولید و توسعه الگوریتم های کارآمد برای حل عددی معادلات دیفرانسیل معمولی مرتبه دوم با شرایط اولیه که دارای جواب های نوسانی یا متناوب هستند، می باشد. الگوریتم مورد نظر از دسته روش های چندگامی خطی و خانواده روش های چندمشتقی است. برتری روش جدید از مقایسه آن با روش های مشابه، از نقطه نظر کارایی، دقت و پایداری با اجرای آنها روی برخی مسائل شناخته شده مانند معادله غیرخطی نامیرا شده دافینگ نشان داده شده است.
A new two-step implicit P-stable Obrechkoff of twelfth algebraic order with vanished phase-lag and its first, second and third derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the second order iniitial value problems that have oscillatory or periodic solutions. This algorithm belongs in the category of the multistep and multiderivative methods. The advantage of the new methods in comparison with similar methods, in terms of efficiency, accuracy and stability, have been showed by the implementation of them in some important problems, including the undamped Duffing equation, etc. -------------- A new two-step implicit P-stable Obrechkoff of twelfth algebraic order with vanished phase-lag and its first, second and third derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the second order iniitial value problems that have oscillatory or periodic solutions. This algorithm belongs in the category of the multistep and multiderivative methods. The advantage of the new methods in comparison with similar methods, in terms of efficiency, accuracy and stability, have been showed by the implementation of them in some important problems, including the undamped Duffing equation, etc.
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