ورقة بحثية
A New Second Order Approximation for Fractional Derivatives with Applications = تقريب جديد من الدرجة الثانية للمشتقات الكسرية مع تطبيقاتها

Nasir. Haniffa M.


 

A New Second Order Approximation for Fractional Derivatives with Applications = تقريب جديد من الدرجة الثانية للمشتقات الكسرية مع تطبيقاتها

Nasir. Haniffa M.

We propose a generalized theory to construct higher order Grünwald type approximations for fractional derivatives. We use this generalization to simplify the proofs of orders for existing approximation forms for the fractional derivative. We also construct a set of higher order Grünwald type approximations for fractional derivatives in terms of a general real sequence and its generating function. From this, a second order approximation with shift is shown to be useful in approximating steady state problems and time dependent fractional diffusion problems. Stability and convergence for a Crank-Nicolson type scheme for this second order approximation are analyzed and are supported by numerical results.

We propose a generalized theory to construct higher order Grünwald type approximations for fractional derivatives. We use this generalization to simplify the proofs of orders for existing approximation forms for the fractional derivative. We also construct a set of higher order Grünwald type approxi...

مادة فرعية

المؤلف : Nasir. Haniffa M.

مؤلف مشارك : Nafa, Kamel

بيانات النشر : Muscat، Sultanate of Oman : Sultan Qaboos Journal of Science، 2018مـ.

التصنيف الموضوعي : العلوم البحتة| .

المواضيع : Mathematics .

Statistics .

الرياضيات .

الإحصاء .

رقم الطبعة : 1

المصدر : Sultan Qaboos University : Muscat، Sultanate of Oman.

لا توجد تقييمات للمادة