Abstract
In this work, we extend the definition of nonic polynomial spline to non-polynomial spline function which depends on arbitrary parameter k. We derived and discussed the formulation and spline relat...
Highlights
In the problems arising in analysis, mechanics, geometry, etc. it is necessary to determine the maximal and minimal of a certain functional; such problems are called variational problems
The direct method of Galerkin and Ritz is investigated by Elsgolts (1977) and Gelfand et al (1963) for solving the calculus of variational problems in general
The observed maximum absolute errors in the solution for different values of n are tabulated in Tables 1–3 and compared with the methods in Jalilian et al (2014), Saadatmandi and Dehghan (2008), Zarebnia and Birjandi (2012), Zarebnia et al (2011) and Zarebnia and Sarvari (2013)
Summary
In the problems arising in analysis, mechanics, geometry, etc. it is necessary to determine the maximal and minimal of a certain functional; such problems are called variational problems. Many authors obtained analytical and numerical methods for the solution of the calculus of variations. The direct method of Galerkin and Ritz is investigated by Elsgolts (1977) and Gelfand et al (1963) for solving the calculus of variational problems in general. Zarebnia et al used B-spline collocation method, non-polynomial spline method and parametric cubic spline method for the solution of problems in calculus of variations (Zarebnia & Birjandi, 2012; Zarebnia, Hoshyar & Sedaghati, 2011; Zarebnia & Sarvari, 2013). Jalilian et al (2014) used non-polynomial spline for the solution of problems in calculus of variations.
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