Quintic hyperbolic nonpolynomial spline and finite difference method for nonlinear second order differential equations and its application

Document Type : Original Article

Authors

Department of Mathematics, Faculty of Mathematics and Computer Science, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi 110 021, India

http://dx.doi.org/10.1016/j.joems.2013.05.009

Abstract

An efficient numerical method based on quintic nonpolynomial spline basis and high
order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.

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