Abstract
In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The problem can easily convert to an optimal control problem. Then a convergent approximate solution is constructed such that the exact boundary conditions are satisfied. The numerical examples and computational results illustrate and guarantee a higher accuracy for this technique.
Highlights
Variational inequality theory has become an effective and powerful tool for studying obstacle and unilateral problems arising in mathematical and engineering sciences
We use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems
This theory has developed into an interesting branch of applicable mathematics, which contains a wealth of new ideas for inspiration and motivation to do research. It has been shown by Kikuchi and Oden [1] that the problem of equilibrium of elastic bodies in contact with a right foundation can be studied in the framework of variational inequality theory
Summary
Variational inequality theory has become an effective and powerful tool for studying obstacle and unilateral problems arising in mathematical and engineering sciences. The computational advantage of this approach is its simple applicability for solving differential equations Such type of penalty function methods have been used quite effectively by Noor and Tirmizi [2], as a basis for obtaining numerical solutions for some obstacle problems. The aim of this paper is to consider the use of quadratic B-spline functions and least square method to develop a numerical method for obtaining smooth approximations for the solution and its derivatives of the general form of a system of second order boundary value problem of the type. Gi : [ai , bi 1] R2 R ( i = 1, 2, 3 ), are given continuous functions, and the parameters 1 and 2 are real finite constants Linear form of such type of systems arise in the study of one dimensional obstacle, unilateral, moving and free boundary value problems,. Up to an error k , the function vk satisfies the differential equation, where k 0 as k
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