TITLE:
Solution of Electrohydrodynamic Flow Equation Using an Orthogonal Collocation Method Based on Mixed Interpolation
AUTHORS:
Shruti Tiwari, Ram K. Pandey
KEYWORDS:
Electrohydrodynamic (EHD) Flow, Weighted Residual Method, Orthogonal Polynomial, Mixed Interpolation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.3,
March
26,
2018
ABSTRACT: 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.