Wavelet-Based Multi-Step Methods for Systems of Differential Equations

الموضوعات

علوم بحتة وطبيعية

الملخص

Wavelets have been widely used in many areas of engineering and mathematics, including the development of multistep algorithms to solve initial value problems (IVPs) in the context of the Galerkin method using Daubechies' wavelets. The main scope of our work is to build a comprehensive framework for solving Systems of Differential equations using the compactly supported wavelets proposed by I. Daubechies. Wavelets are mathematical functions that decompose data into distinct frequency components, and each element is analyzed with a resolution that matches its scale. Compact support of Daubechies wavelets is key in allowing them to be computationally efficient for high-dimensional problems. Finding the Inner products is difficult since Daubechies' wavelets lack precise equations, despite having a high approximation quality. This challenge can be addressed by considering the order of approximation of the wavelets to derive implicit multistep methods that have comparable stability properties to other methods. Numerical examples are given to verify the accuracy and efficiency of the proposed framework for solving systems of differential equations.

روابط وملفات

التعريف والنوع

رقم الوثيقة

07478079-0e6a-4aa4-a54b-53aedd1cb132

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل ماجيستير

نوع الملف

pdf text

أسماء الملفات

1084843_2.pdf

بيانات النشر

ترجمة العنوان

طرق متعددة الخطوات لأنظمة المعادلات التفاضلية اعتمادا على المويجات

ألقاب المؤلفين

[{"name_ar":"Mohamed Ali Hajji","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"Rashad Assad Hijji","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

English

المصدر والدورية

اسم المصدر

Wavelet-Based Multi-Step Methods for Systems of Differential Equations

المحتوى والصفحات

عدد الصفحات

0

كلمات الباحثين

Daubechies’ Wavelets, Wavelet Basis, Multiresolution Analysis (MRA), Multi-Step Methods, Systems of differential equations, Galerkin Method.

إشراف وإعداد

الإشراف

Mohamed Ali Hajji

الإعداد

Rashad Assad Hijji

الاقتباسات الببليوغرافية