Solving steady heat transfer problems via Kashuri Fundo transform

Pekera, Haldun; ÇUHA, Fatma Aybike; PEKER, Bilge

doi:10.2298/tsci2204011p

Cited by 8 publications

(4 citation statements)

References 17 publications

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“…Since the equations obtained as a result of the transformation usually have a more standardized and easier to understand form, the analytical or numerical solutions of the equations become easier and more general. There are many different studies in the literature that reveal the accuracy of these statements [11][12][13][14][15][16][17][18][19][20][21]. There are many studies that show that it gives effective results when used by blending with different methods to reach solutions of nonlinear and fractional differential equations [22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Newton s Law of Cooling Equation via Kashuri Fundo Transform

Peker,

Çuha,

Peker

2024

neufmbd

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Geçmişte olduğu gibi günümüzde de fiziksel olayların anlaşılması, doğru bir şekilde yorumlanabilmesi ve modellenmesi gelişmiş matematiksel yöntemlerin kullanılmasını gerektirir. Bu bağlamda, Newton'un soğuma yasası gibi ısı transferi problemlerinin çözümü, integral dönüşümü gibi güçlü matematiksel araçlarla karmaşık hesaplamalara gerek kalmadan, doğru, güvenilir ve kolaylıkla elde edilir. Newton'un soğuma yasası bir cismin sıcaklığının çevresel sıcaklıkla nasıl etkileşime girdiğini ve zaman içinde nasıl değiştiğini diferensiyel denklem modelleriyle ifade eder. Değişkenler ve değişim hızları arasındaki karmaşık ilişkileri ifade eden bu denklemler, fizikçilerin kesin matematiksel modeller formüle etmelerine olanak tanıyarak, fiziksel sistemlerin davranışlarına ilişkin doğru yorumlar yapılmasını sağlarlar. Diferensiyel denklemlerin çözümlerini elde etmeye yönelik hesaplamalar, cebirsel denklemlere ilişkin hesaplamalardan daha karmaşık olabilir. Bundan dolayı, bu denklemlerin çözümlerini elde etmek için farklı yöntemler kullanılmıştır. Bu makalede, Newton'un soğuma yasasının integral dönüşümlerinin bir çeşidi olan Kashuri Fundo dönüşümü ile çözümünü ve bu yaklaşımın fizik, biyokimya, ekonomi, finans, mühendislik vb. alanlarda yer alan farklı matematiksel modellerin çözümlerine ulaşmada kullanılabilecek etkili ve güvenilir bir yöntem olduğunu ortaya koyuyoruz.

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Section: Introductionmentioning

confidence: 99%

Analytical Solution of Newton s Law of Cooling Equation via Kashuri Fundo Transform

Peker,

Çuha,

Peker

2024

neufmbd

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“…To solve systems of ordinary differential equations, Zamil and Kuffi [8] applied Sadiq and the complex Sadiq transforms. Peker et al (9)(10)(11)(12)(13)(14) utilized the Kashuri Fundo transform to solve various models, including steady heat transfer, decay, chemical reactions, Bratu's problem, Michaelis-Menten's biochemical reaction model, population growth, and mixing problems. Through these applications, they effectively showcased the capability of the transform in obtaining solutions for ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of Cardiovascular Models by using Upadhyaya Transform

Thakur,

Kuffi

2024

Jour. Kufa Math. Comp.

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In many practical fields, such as engineering, physics, chemistry, biology, psychology, economics, and finance, processes are simulated using differential equations. These models solutions, in contrast to algebraic equations, may be more intricate. In order to get at the solutions to these models, it is easy to employ integral transformations. In this paper, we use the Upadhyaya transform to obtain accurate solutions to two cardiovascular models. It is obvious that the Upadhyaya transform is an effective, dependable, and simple technique for solving differential equations.

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“…Helmi et al [17], Singh [18], Dhange [19], and Güngör [20] investigated various applications of Kashuri Fundo transformation. Later, Peker et al [21][22][23][24][25][26] applied this transform to the models, namely steady heat transfer, decay, some chemical reaction, one-dimensional Bratu's problem, Michaelis-Menten's biochemical reaction model, population growth and mixing problem to demonstrate the competence of the Kashuri Fundo transform in reaching solutions of ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform

Peker

ÇUHA

2023

Journal of New Theory

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Differential equations refer to the mathematical modeling of phenomena in various applied fields, such as engineering, physics, chemistry, astronomy, biology, psychology, finance, and economics. The solutions of these models can be more complicated than those of algebraic equations. Therefore, it is convenient to use integral transformations to attain the solutions of these models. In this study, we find exact solutions to two cardiovascular models through an integral transformation, namely the Kashuri Fundo transform. It can be observed that the considered transform is a practical, reliable, and easy-to-use method for obtaining solutions to differential equations.

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Solving steady heat transfer problems via Kashuri Fundo transform

Cited by 8 publications

References 17 publications

Analytical Solution of Newton s Law of Cooling Equation via Kashuri Fundo Transform

Analytical Solution of Newton s Law of Cooling Equation via Kashuri Fundo Transform

Exact Solutions of Cardiovascular Models by using Upadhyaya Transform

Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform

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