PAPER ON ANALYTICAL SOLUTION OF HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS

Authors

  • Chetan Rathod Lecturer, Department Of Mathematics, Swami Vivekanand Degree College Muddebihal-586212

DOI:

https://doi.org/10.29121/shodhkosh.v2.i2.2021.3654

Keywords:

Partial Differential Equation, Separation of Variables, Shape Function, Power Series

Abstract [English]

For a long time, detachment of variable is perceived as one of the most remarkable strategies for settling straight incomplete differential conditions PDEs. The current paper proposes scientific answer for higher request homogeneous fractional differential conditions PDEs under determined limit conditions BCs inside a rectangular space. Partition of factors and basic variables, first and foremost, are utilized to decrease the given incomplete differential condition PDE to a common differential condition Tribute. After representative controls, a power series development of the obscure capability is used to make the logical arrangement. The current paper is an extraordinary instance of partition of factors which depend on dispensing with one variable to settle the PDE on the other variable. The proposed shut structure arrangement introduced here lessens the work consumed for carry out the option mathematical arrangements. The viability of the got strategy demonstrates the ability to give a scientific arrangement beating the intricacy of limit conditions and blended subordinates in the arrangement of higher request straight PDE.

References

H. Ugail, Partial Differential Equations for Geometric Design, Springer Verlag, London, UK, 2011. DOI: https://doi.org/10.1007/978-0-85729-784-6

A. D. Polyanin, Handbook of Nonlinear Partial Differential Equations, 1st Edition, Chapman and Hall/CRC, New York, 2003. DOI: https://doi.org/10.1201/9780203489659

T. Kobayashi, N. Kawashima and Y. Ochiai, Image processing by interpolation using polyharmonic function and increase in processing speed, IEEJ Transactions on Electrical and Electronic Engineering, 6(S1), S1-S6, 2011. DOI: https://doi.org/10.1002/tee.20614

L. H. You, J. Changa, X. S. Yanga J. J. and Zhanga, Solid modelling based on sixth order partial differential equations. Computer-Aided Design, 43(6), 720-729, 2011. DOI: https://doi.org/10.1016/j.cad.2011.01.021

M. H. Martin, A Generalization of the Method of Separation of Variables, Indiana Univ Math J, 2, 315-327, 1953. DOI: https://doi.org/10.1512/iumj.1953.2.52017

E. Karimov and S. Pirnafasov. Higher Order Multi-Term Time- Fractional Partial Differential Equations Involving Caputo-Fabrizo Derivatives. Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 243, pp. 1-11.

I.V. Rakhmelevich, Multi-Dimensional Partial Differential Equations with Power Nonlinearities in the First Derivatives, Ufa Mathematical Journal. Vol. 9. No 1 (2016). P. 98-108. DOI: https://doi.org/10.13108/2017-9-1-98

W. N. Everitt and B. T. Johansson, Quasi-separation of the Biharmonic Partial Differential Equation, IMA Journal of Applied Mathematics (2009) 74, 85−709 DOI: https://doi.org/10.1093/imamat/hxp016

A. S. Berdyshev and B. J. Kadirkulov , On a Nonlocal Problem for a Fourth-Order Parabolic Equation with the Fractional Dzhrbashyan–Nersesyan Operator, Differentially Uravneniya, 2016, Vol. 52, No. 1, pp. 123–127. DOI: https://doi.org/10.1134/S0012266116010109

Xiang Liua , Xiao Liua and Suchao Xie . A highly accurate analytical spectral flexibility formulation for buckling and wrinkling of orthotropic rectangular plates. International Journal of Mechanical Sciences Volume 168,15 February 2020, 105311 DOI: https://doi.org/10.1016/j.ijmecsci.2019.105311

A. H. A. Hassan and Naci Kurgan. Buckling of thin skew isotropic plate resting on Pasternak elastic foundation using extended Kantorovich method. www. elsevier.com/ locate/heliyon . Heliyon 6 (2020) e04236. DOI: https://doi.org/10.1016/j.heliyon.2020.e04236

Xiang Liu, Xiao Liu and Wei Zhou. An analytical spectral stiffness method for buckling of rectangular plates on Winkler foundation subject to general boundary conditions. Applied Mathematical Modeling 86 (2020) 36–53. DOI: https://doi.org/10.1016/j.apm.2020.05.010

Michael Doschoris, Towards a Generalization of the Separation of Variables Technique, Methods and Applications of Analysis. Vol. 19, No. 4, pp. 381–402, December 2012. DOI: https://doi.org/10.4310/MAA.2012.v19.n4.a4

Travis Askham, A stabilized separation of variables method for the modified biharmonic equation, Journal of Scientific Computing, Vol.76, pp1674–1697(2018). DOI: https://doi.org/10.1007/s10915-018-0679-9

Hsieh M-C, Hwu C. Anisotropic elastic plates with holes/cracks/inclusions subjected to out-of-plane bending moments. Int J Solids Struct 2002;39(19): 4905-4905. DOI: https://doi.org/10.1016/S0020-7683(02)00335-9

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Published

2022-12-31

How to Cite

Rathod, C. (2022). PAPER ON ANALYTICAL SOLUTION OF HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS. ShodhKosh: Journal of Visual and Performing Arts, 2(2), 281–288. https://doi.org/10.29121/shodhkosh.v2.i2.2021.3654