يك روش جديد دوگامي متقارن ابرشكف P-پايدار از مرتبه جبري دوازدهم براي حل عددي مسائل مقدار اوليه مرتبه دوم

A new symmetric two-step P-stable Obrechkoff method with 12 algebraic order for the numerical solution of second-order IVPs

در اين مقاله، يك روش جديد دوگامي خطي ابرشكف ضمني از مرتبه جبري دوازدهم با استفاده از تكنيك صفر كردن فازتاخيري ومشتق هاي مراتب اول، دوم و سوم آن توليد و مورد تجزيه و تحليل قرار مي گيرد. هدف اصلي اين مقاله، توليد و توسعه الگوريتم هاي كارآمد براي حل عددي معادلات ديفرانسيل معمولي مرتبه دوم با شرايط اوليه كه داراي جواب هاي نوساني يا متناوب هستند، مي باشد. الگوريتم مورد نظر از دسته روش هاي چندگامي خطي و خانواده روش هاي چندمشتقي است. برتري روش جديد از مقايسه آن با روش هاي مشابه، از نقطه نظر كارايي، دقت و پايداري با اجراي آنها روي برخي مسائل شناخته شده مانند معادله غيرخطي ناميرا شده دافينگ 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.