scholarly journals Numerical Solution of Two-Point Boundary Value Problems by Interpolating Subdivision Schemes

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Ghulam Mustafa ◽  
Syeda Tehmina Ejaz
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Point Boundary ◽  
Approximation Properties ◽  
Third Order ◽  
Continuous Solutions ◽  
Subdivision Schemes ◽  
Numerical Examples

A numerical interpolating algorithm of collocation is formulated, based on 8-point binary interpolating subdivision schemes for the generation of curves, to solve the two-point third order boundary value problems. It is observed that the algorithm produces smooth continuous solutions of the problems. Numerical examples are given to illustrate the algorithm and its convergence. Moreover, the approximation properties of the collocation algorithm have also been discussed.

scholarly journals Alternative methods for solving nonlinear two-point boundary value problems

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 371-374
Author(s):  
Fateme Ghomanjani ◽  
Stanford Shateyi
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Bernstein Polynomials ◽  
Nonlinear Problems ◽  
Alternative Methods ◽  
Point Boundary ◽  
Numerical Examples ◽  
Curve Method ◽  
Linear And Nonlinear

Abstract In this sequel, the numerical solution of nonlinear two-point boundary value problems (NTBVPs) for ordinary differential equations (ODEs) is found by Bezier curve method (BCM) and orthonormal Bernstein polynomials (OBPs). OBPs will be constructed by Gram-Schmidt technique. Stated methods are more easier and applicable for linear and nonlinear problems. Some numerical examples are solved and they are stated the accurate findings.

A Collocation Method for Global Approximation of General Second Order BVPs

2007 ◽  
Vol 3 (1) ◽  
pp. 23-34 ◽  
Author(s):  
F. Costabile ◽  
A. Napoli
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Collocation Method ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Global Approximation ◽  
Numerical Examples

For the numerical solution of the second order nonlinear two-point boundary value problems a family of polynomial global methods is derived.Numerical examples provide favorable comparisons with other existing methods.

scholarly journals Numerical Solution for Third-Order Two-Point Boundary Value Problems with the Barycentric Rational Interpolation Collocation Method

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Qian Ge ◽  
Xiaoping Zhang
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Collocation Method ◽  
Boundary Value ◽  
Rational Interpolation ◽  
Point Boundary ◽  
Third Order ◽  
The Third ◽  
The Matrix ◽  
Barycentric Rational Interpolation

The numerical solution for a kind of third-order boundary value problems is discussed. With the barycentric rational interpolation collocation method, the matrix form of the third-order two-point boundary value problem is obtained, and the convergence and error analysis are obtained. In addition, some numerical examples are reported to confirm the theoretical analysis.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

scholarly journals Solving nonlinear third-order three-point boundary value problems by boundary shape functions methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ji Lin ◽  
Yuhui Zhang ◽  
Chein-Shan Liu
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Initial Conditions ◽  
Boundary Value ◽  
Accurate Solution ◽  
Point Boundary ◽  
Third Order ◽  
Boundary Shape ◽  
Free Function ◽  
New Algorithms

AbstractFor nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified three-point boundary conditions. We construct a boundary shape function (BSF), which is designed to automatically satisfy the boundary conditions and can be employed to develop new algorithms by assigning two different roles of free function in the BSF. In the first algorithm, we let the free functions be complete functions and the BSFs be the new bases of the solution, which not only satisfy the boundary conditions automatically, but also can be used to find solution by a collocation technique. In the second algorithm, we let the BSF be the solution of the BVP and the free function be another new variable, such that we can transform the BVP to a corresponding initial value problem for the new variable, whose initial conditions are given arbitrarily and terminal values are determined by iterations; hence, we can quickly find very accurate solution of nonlinear third-order three-point BVP through a few iterations. Numerical examples confirm the performance of the new algorithms.

scholarly journals On the Solvability of Nonlinear Third-Order Two-Point Boundary Value Problems

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 62
Author(s):  
Ravi P. Agarwal ◽  
Petio S. Kelevedjiev ◽  
Todor Z. Todorov
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Barrier Strips

Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] —solutions to various two-point boundary value problems for the equation x ‴ = f ( t , x , x ′ , x ″ ) . We give also some results guaranteeing positive or non-negative, monotone, convex or concave solutions.

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