طريقتان عدديتان لإيجاد الجذور التقريبية الحقيقية والعقدية للمعادلات غير الخطية
Abstract
تم في هذا البحث تقديم طريقتين عدديتين لإيجاد الجذور الحقيقية البسيطة والمضاعفة m مرة بالإضافة إلى الجذور العقدية للمعادلات غير الخطية من الشكل . تعتمد الطريقة الأولى على تقريبات الدالة f بكثيرات حدود تايلور من الدرجة الثالثة حول الجذور المطلوب إيجادها، ثم استخدام طريقة كوردانو وتحويلها إلى علاقات ذات صياغة تكرارية. أما الطريقة الثانية المقترحة فتعتمد على تعديلات لطريقة هالي. تم توصيف الطريقتين المقترحتين بالخوارزميات اللازمة وتنفيذها باستخدام برنامج Mathemtica في النسخة 9. اختُبِرتْ فعالية الطريقتين المقدمتين بتطبيقهما لإيجاد الجذور التقريبية العقدية والحقيقية البسيطة والمضاعفة m مرة لبعض المسائل، حيث تشير النَتائِج العددية إلى فعالية ودقة الطريقتين بالمقارنة مع بعض الطرائق الأخرى. In this paper, we introduce two numerical methods for finding the simple real roots, multiple real roots and complex roots of the nonlinear equations . The first method is based on approximations the function f by third Taylor polynomial about the roots of the nonlinear equations. After that, Gordano method is used which is transformed to iterative method. The second method is based on modifies of Halley method . The two algorithms are designed of the presented methods, and programming Mathematica Version 9 is used. Numerical experiments are given for finding the simple real roots, multiple real roots and complex roots of some test problems. Comparisons of the results obtained by two methods with other methods illustrate the efficiency and highly accurate of the proposed methods.Downloads
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