Numerical solution of a singularly perturbed Fredholm integro differential
equation with Robin boundary condition

Kamiş, Okan; AYDOS, Latif; KUDU, Mustafa; AMIRALIYEV, Gabil M.; Durmaz, Muhammet Enes

doi:10.3906/mat-2109-11

Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition

Okan KAMİŞ, (Gazi Üniversitesi, Sağlık Bilimleri Enstitüsü, Beden Eğitimi ve Spor Bölümü, Ankara, Türkiye)

Muhammet Enes DURMAZ, (Kırklareli Üniversitesi, Teknik Bilimler Meslek Yüksekokulu, Bilgi Teknolojileri Bölümü, Kırklareli, Türkiye)

Latif AYDOS, (Gazi Üniversitesi, Spor Bilimleri Fakültesi, Beden Eğitimi ve Spor Bölümü, Ankara, Türkiye)

Gabil M. AMİRALİYEV, (Erzincan Binali Yıldırım Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Erzincan, Türkiye)

Mustafa KUDU (Erzincan Binali Yıldırım Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Erzincan, Türkiye)

Turkish Journal of Mathematics

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Yıl: 2022 Cilt: 14 Sayı: 2 Sayfa Aralığı: 207 - 224 Metin Dili: İngilizce DOI: 10.3906/mat-2109-11 İndeks Tarihi: 19-07-2022

Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition

Öz:

In this paper, we deal with singularly perturbed Fredholm integro differential equation (SPFIDE) with mixed boundary conditions. By using interpolating quadrature rules and exponential basis function, fitted second order difference scheme has been constructed on a Shishkin mesh. The stability and convergence of the difference scheme have been analyzed in the discrete maximum norm. Some numerical examples have been solved and numerical outcomes are obtained.

Anahtar Kelime:

Resistance Exercise with Blood Flow Restriction: A Novel Training Technique to Maximize Strength and Hypertrophy: A Brief Review

Öz:

Low-load resistance exercise with blood flow restriction has been known to stimulate muscle development that is comparable to conventional High-load Resistance Exercise. Resistance exercise with blood flow restriction is a pretty new training technique that can be an option to High-load Resistance Exercise for increasing muscle mass and strength not only in athletes but also in healthy people and elderly people, or rehabilitation for injured athletes with load restrictions. This brief review study aims to summarize the existing literature concerning the basic principles of resistance exercise with blood flow restriction and to provide a brief description of blood flow restriction training to maximize strength and hypertrophy. Blood flow restriction training can be performed when High-load Resistance Exercise is not tolerated be- cause of pain or other contraindications such as absolute weight-bear- ing restrictions, for instance after surgical procedures to regain strength and muscle mass. High-load Resistance Exercise is associated with high mechanical tension, however in some cases, this is not warranted. In these cases, resistance exercise with blood flow restriction seems to be a better option. Consequently, blood flow restriction training should not replace High-load Resistance Exercise for the general public or un- injured athletes, but blood flow restriction training can be used as an al- ternating training tool or in situations where High-load Resistance Exercise is inadvisable.

Anahtar Kelime:

Kan Akışı Kısıtlamalı Direnç Egzersizi: Kuvvet ve Hipertrofiyi En Üst Düzeye Çıkarmak İçin Yeni Bir Antrenman Tekniği: Kısa Derleme

Öz:

Kan akışı kısıtlama ile birlikte kombine olarak yapılan düşük yüklü direnç egzersizlerinin, geleneksel yüksek yüklü direnç egzersiz- leri ile karşılaştırılabilir kas büyümesi sağladığı gösterilmiştir. Kan akışı kısıtlama antrenmanı, sadece sporcularda değil, aynı zamanda sağlıklı insanlarda, yaşlı erişkinlerde veya yüksek yüklü antrenmanlara bağlı yaralanma sorunları olan sporcularda kas boyutunu ve kuvvetini geliş- tirmek için yüksek yüklü direnç antrenmanına alternatif olabilecek ol- dukça yeni bir antrenman tekniğidir. Bu kısa derleme çalışması, kan akışı kısıtlama antrenmanının temel ilkeleri ile ilgili mevcut literatürü özetlemeyi ve kuvvet ve hipertrofiyi en üst düzeye çıkarmak için kan akışı kısıtlama antrenmanının kısa bir tanımını sağlamayı amaçlamak- tadır. Kan akışı kısıtlama antrenmanı, yüksek yüklü direnç antrenman- larının tolere edilemediği durumlarda, kuvvet ve hipertrofi kazandırmak amacıyla yapılabilir. Kan akışı kısıtlama antrenmanı, ağrı veya ağırlık kaldıramama kısıtlamaları gibi diğer kontraendikasyonlar nedeniyle yüksek yüklü direnç egzersizleri tolere edilmediğinde, örneğin kuvvet ve kas kütlesini yeniden kazanmak için cerrahi prosedürlerden sonra yapılabilir. Yüksek yüklü direnç egzersizleri yüksek mekanik gerilim ile ilişkilidir, ancak bazı durumlarda yüksek yükü tolere etmek müm- kün olmayabilir, bu gibi durumlarda kan akışı kısıtlamalı direnç eg- zersizi iyi bir seçenek olarak görülebilir. Sonuç olarak, kan akışı kısıtlama antrenman metodu, genel popülasyon ve sakatlık geçirmemiş sporcular için yüksek yüklü direnç egzersizlerinin yerini almamalıdır, ancak kan akışı kısıtlama antrenmanı, alternatif bir antrenman aracı ola- rak veya yüksek yüklü direnç egzersizlerinin tavsiye edilmediği du- rumlarda kullanılabilir

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	Durmaz M, Kamiş O, AMIRALIYEV G, AYDOS L, KUDU M (2022). Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. , 207 - 224. 10.3906/mat-2109-11
Chicago	Durmaz Muhammet Enes,Kamiş Okan,AMIRALIYEV Gabil M.,AYDOS Latif,KUDU Mustafa Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. (2022): 207 - 224. 10.3906/mat-2109-11
MLA	Durmaz Muhammet Enes,Kamiş Okan,AMIRALIYEV Gabil M.,AYDOS Latif,KUDU Mustafa Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. , 2022, ss.207 - 224. 10.3906/mat-2109-11
AMA	Durmaz M,Kamiş O,AMIRALIYEV G,AYDOS L,KUDU M Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. . 2022; 207 - 224. 10.3906/mat-2109-11
Vancouver	Durmaz M,Kamiş O,AMIRALIYEV G,AYDOS L,KUDU M Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. . 2022; 207 - 224. 10.3906/mat-2109-11
IEEE	Durmaz M,Kamiş O,AMIRALIYEV G,AYDOS L,KUDU M "Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition." , ss.207 - 224, 2022. 10.3906/mat-2109-11
ISNAD	Durmaz, Muhammet Enes vd. "Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition". (2022), 207-224. https://doi.org/10.3906/mat-2109-11

APA	Durmaz M, Kamiş O, AMIRALIYEV G, AYDOS L, KUDU M (2022). Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. Turkish Journal of Mathematics, 14(2), 207 - 224. 10.3906/mat-2109-11
Chicago	Durmaz Muhammet Enes,Kamiş Okan,AMIRALIYEV Gabil M.,AYDOS Latif,KUDU Mustafa Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. Turkish Journal of Mathematics 14, no.2 (2022): 207 - 224. 10.3906/mat-2109-11
MLA	Durmaz Muhammet Enes,Kamiş Okan,AMIRALIYEV Gabil M.,AYDOS Latif,KUDU Mustafa Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. Turkish Journal of Mathematics, vol.14, no.2, 2022, ss.207 - 224. 10.3906/mat-2109-11
AMA	Durmaz M,Kamiş O,AMIRALIYEV G,AYDOS L,KUDU M Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. Turkish Journal of Mathematics. 2022; 14(2): 207 - 224. 10.3906/mat-2109-11
Vancouver	Durmaz M,Kamiş O,AMIRALIYEV G,AYDOS L,KUDU M Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. Turkish Journal of Mathematics. 2022; 14(2): 207 - 224. 10.3906/mat-2109-11
IEEE	Durmaz M,Kamiş O,AMIRALIYEV G,AYDOS L,KUDU M "Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition." Turkish Journal of Mathematics, 14, ss.207 - 224, 2022. 10.3906/mat-2109-11
ISNAD	Durmaz, Muhammet Enes vd. "Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition". Turkish Journal of Mathematics 14/2 (2022), 207-224. https://doi.org/10.3906/mat-2109-11