رویکردی نوین در بکارگیری روش تحلیل هموتوپی
محورهای موضوعی : آنالیز عددی
1 - گروه ریاضی، واحد علی آباد کتول، دانشگاه آزاد اسلامی، علی آباد کتول، ایران
کلید واژه: Approximate solution, Homotopy analysis method, Series solution, Nonlinear initial value problem,
چکیده مقاله :
یکی از روش های بسیار مهم در حل مسائل خطی و غیرخطی، روش تحلیل هموتوپی است که توسط لیائو در سال 1992 مطرح گردید. هدف اصلی این مقاله، بهبود روش تحلیل هموتوپی است که این نوع بهبود یافته را روش تحلیل هموتوپی متوالی نامگذاری نموده ایم. جهت مقایسه ی نتایج به دست آمده توسط روش تحلیل هموتوپی و نوع متوالی آن، چندین مثال عددی ارائه شده است که نتایج نشان می دهند، حجم محاسبات در روش تحلیل هموتوپی متوالی نسبت به نوع معمولی آن کمتر است. همچنین، برخلاف روش تحلیل هموتوپی، جواب های عددی به دست آمده توسط روش تحلیل هموتوپی متوالی در یک محدوده ی نسبتاً وسیعی رضایتبخش هستند. بنابراین، با توجه به روش تحلیل هموتوپی متوالی، می توان انواع مختلف معادلات ریاضی خطی و غیرخطی و همچنین معادلاتی غیر خطی که در سایر رشته های علمی مانند فیزیک و مکانیک به وجود می آیند را به صورت عددی حل نمود.
One of the most important methods for solving linear and nonlinear problems is the homotopic analysis method, which was proposed by Liao in 1992. The main purpose of this paper is to present a modification of homotopy analysis method (HAM), which is called successive homotopy analysis method (SHAM). Several numerical examples are presented to present a comparison between the results obtained by homotopy analysis method and its successive type. The results show that the calculation volume in the successive homotopy analysis method is less that the homotopy analysis method. Also, unlike the homotopy analysis method, the numerical solutions obtained by the successive homotopy analysis method are satisfactory over a relatively wide range. So, by using the successive homotopy analysis method, various types of linear and nonlinear mathematical equations and also some nonlinear equations which are obtained in other scientific branches, for instance physics, mechanics and etc, can be solved numerically.
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