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.

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.

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 Application of Optimal Homotopy Asymptotic Method to Some Well-Known Linear and Nonlinear Two-Point Boundary Value Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Muhammad Asim Khan ◽  
Shafiq Ullah ◽  
Norhashidah Hj. Mohd Ali
Keyword(s):  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Homotopy Perturbation Method ◽  
Boundary Value ◽  
Point Boundary ◽  
Small Perturbations ◽  
Homotopy Perturbation ◽  
Optimal Homotopy Asymptotic Method ◽  
Linear And Nonlinear ◽  
Semianalytical Method

The objective of this paper is to obtain an approximate solution for some well-known linear and nonlinear two-point boundary value problems. For this purpose, a semianalytical method known as optimal homotopy asymptotic method (OHAM) is used. Moreover, optimal homotopy asymptotic method does not involve any discretization, linearization, or small perturbations and that is why it reduces the computations a lot. OHAM results show the effectiveness and reliability of OHAM for application to two-point boundary value problems. The obtained results are compared to the exact solutions and homotopy perturbation method (HPM).

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