Solutions of nonlinear systems by reproducing kernel method

Volume 10, Issue 8, pp 4408--4417 http://dx.doi.org/10.22436/jnsa.010.08.33

Publication Date: August 25, 2017 Submission Date: May 17, 2017

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Authors

Ali Akgül - Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey. Yasir Khan - Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia. Esra Karatas Akgül - Gelibolu Piri Reis Vocational School, Canakkale Onsekiz Mart University, 17100, Canakkale, Turkey. Dumitru Baleanu - Department of Mathematics and Computer Sciences, Art and Science Faculty, Cankaya University, TR-06300 Ankara, Turkey. - Department of Mathematics, Institute of Space Sciences, Bucharest, Romania. Maysaa Mohamed Al Qurashi - Department of Mathematics, King Saud University, Riyadh 12364, Saudi Arabia.

Abstract

A novel approximate solution is obtained for viscoelastic fluid model by reproducing kernel method (RKM). The resulting equation for viscoelastic fluid with magneto-hydrodynamic flow is transformed to the nonlinear system by introducing the dimensionless variables. Results are presented graphically to study the efficiency and accuracy of the reproducing kernel method. Results show that this method namely RKM is an efficient method for solving nonlinear system in any engineering field.

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Keywords

• Reproducing kernel method
• series solutions
• nonlinear systems.

MSC

•  47B32
•  46E22
•  35M32
•  74S30

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