Numerical Scheme based on Non-polynomial Spline Functions for the System of Second Order Boundary Value Problems arising in Various Engineering Applications (original) (raw)
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Applied Mathematics and Computation, 2006
A quadratic non-polynomial spline functions based method is developed to find approximations solution to a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. The present approach has less computational cost and gives better approximations than those produced by other collocation, finite-difference and spline methods. Convergence analysis of the method is discussed. A numerical example is given to illustrate practical usefulness of the new method.
Studia Universitatis Babes-Bolyai Matematica, 2020
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Applied Mathematics and Computation, 2006
We use a cubic spline equivalent nonpolynomial spline functions to develop a numerical method for computing approximations to the solution of a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. We show that the present method gives approximations which are better than those produced by other collocation, finite difference and spline methods. Convergence analysis of the method is discussed. A numerical example is given to illustrate practical usefulness of our method.
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Journal of Optimization Theory and Applications, 2003
We use parametric cubic spline functions to develop a numerical method for computing approximations to the solution of a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. We show that the present method gives approximations which are better than those produced by other collocation, finite-difference, and spline methods. A numerical example is given to illustrate the applicability and efficiency of the new method.
Non-Polynomial Spline Method for Solving Nonlinear Two Point Boundary Value Problems
Ethiopian Journal of Education and Sciences, 2019
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BIT, 1979
A numerical method, using spline functions of degree five, for obtaining approximate solutions to initial value problems is presented. It is shown that the method is stable and the convergence is analysed. Some numerical experiments are included. Introduction. Recently we presented in [4] a method for construction of global approximations to the initial value problems in ordinary differential equations, using interpolate, piecewise polynomial functions of degree three, where we achieve convergence of order four. Now, we work on the same initial value problem with piecewise polynomial functions of degree five, belonging to C2[a, b] and with the collocation method. We prove the convergence and stability of the method achieving approximations of order six.
Convergence Analysis of Spline Solutions for Special Nonlinear Two -Order Boundary Value Problems
2009
The smooth approximate solution of nonlinear second order boundary value problems are developed by using non-polynomial quintic spline function. A new approach convergence analysis of the presented methods is discussed. Some examples are considered in our references. By considering the maximum absolute errors in the solution at grid points and tabulated in tables for different choices of step size. We conclude that our presented method produces the accurate results in comparison with those obtained by the existing methods.