engleski

New class of finite functions in the numerical analysis of the process on the continuum

This paperpresents a new class of finite functions which posses the property of infinite smoothness and are referred to as Rbf - Rvachevs basis functions. Rbf functions retain the property of universality in a waysimilar to algebraic and trigonometric polynomials and, at the same time, thay preserve the properties of a practical application of splines. The properties of these functions classify them between classical polynomials and spline functions ; they complete a set of elementary functions. The application of Rbf functions as basis functions in approximate methods makes it possible to avoid various numerical difficulties frequently present in the previously applied basis functions and to overcome the main constraints of classical and spline functions. In the numerical procedure it is possible to use directly all degrees of derivations of Rbf basis functions as required by the differential equation and boundary conditions. The application of the strong formulation makes the numerical procedure much more efficient ; at the same time, numerical integration can be avoided. The new class of finite basis functions makes it possible for all the fields derived from the approximate solution to be expressed by an infinite function in the considered areas. The universality property of Rbf functions enables the use of numerical solutions with a given accuracy, which makes Rbf functions more efficient than all previously known finite functions. Exceptional approximation properties of the new class of Rbf basis functions are illustrated by the examples of a nonlinear analysis. By applying the Rbf functions a numerical model was developed which makes possible efficient determination f a nonlinear response of the structure with a high degree of accuracy and quality of the approximate solution. The advantages of Rbf functions become most prominent in the numerical analysis of nonlinear behaviour of the structure since they ensure high accuracy and stability of the numerical procedure.

finite functions; numerical analysis; continuum

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