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Solution of Electrohydrodynamic Flow Equation Using an Orthogonal Collocation Method Based on Mixed Interpolation

Solution of Electrohydrodynamic Flow Equation Using an Orthogonal Collocation Method Based on Mixed Interpolation

作     者:Shruti Tiwari Ram K. Pandey 

作者机构:Department of Mathematics and Statistics Dr. H.S. Gour Vishwavidyalaya Sagar India 

出 版 物:《Journal of Applied Mathematics and Physics》 (应用数学与应用物理(英文))

年 卷 期:2018年第6卷第3期

页      面:573-587页

学科分类:07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主  题:Electrohydrodynamic (EHD) Flow Weighted Residual Method Orthogonal Polynomial Mixed Interpolation 

摘      要:In this Paper, we have proposed a new weighted residual method known as orthogonal collocation-based on mixed interpolation (OCMI). Mixed interpolation uses the classical polynomial approximation with two correction terms given in the form of sine and cosine function. By these correction terms, we can control the error in the solution. We have applied this approach to a non-linear boundary value problem (BVP) in ODE which governs the electrohydrodynamic flow in a cylindrical conduit. The solution profiles shown in the figures are in good agreement with the work of Paullet (1999) and Ghasemi et al. (2014). Our solution is monotonic decreasing and satisfies , where, α governs the strength of non-linearity and for large values of α solutions are . The residual errors are given in Table 1 and Table 2 which are significantly small. Comparison of residual errors between our proposed method, Least square method and Homotopy analysis method is also given and shown via the Table 3 where as the profiles of the residual error are depicted in Figures 4-8. Table and graphs show that efficiency of the proposed method. The error bound and its L2-norm with relevant theorems for mixed interpolation are also given.

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