scholarly journals Numerical Solutions of a Class of Second Order Boundary Value Problems on Using Bernoulli Polynomials

2011 ◽  
Vol 02 (09) ◽  
pp. 1059-1067 ◽  
Author(s):  
Md. Shafiqul Islam ◽  
Afroza Shirin
Keyword(s):  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Bernoulli Polynomials ◽  
Second Order

scholarly journals Numerical Solutions of System of Second Order Boundary Value Problems using Galerkin Method

2018 ◽  
Vol 37 ◽  
pp. 161-174
Author(s):  
Mahua Jahan Rupa ◽  
Md Shafiqul Islam
Keyword(s):  
Boundary Value Problems ◽  
Legendre Polynomials ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Second Order ◽  
Basis Functions ◽  
Reasonable Accuracy ◽  
Weighted Residual Method ◽  
One Dimensional

In this paper we derive the formulation of one dimensional linear and nonlinear system of second order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. Here we use Bernstein and Legendre polynomials as basis functions. The proposed method is tested on several examples and reasonable accuracy is found. Finally, the approximate solutions are compared with the exact solutions and also with the solutions of the existing methods.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 161-174

scholarly journals NUMERICAL SOLUTION OF A CLASS OF NONLINEAR SYSTEM OF SECOND-ORDER BOUNDARY-VALUE PROBLEMS: A FOURTH-ORDER CUBIC SPLINE APPROACH

2015 ◽  
Vol 20 (5) ◽  
pp. 681-700 ◽  
Author(s):  
Suheil A. Khuri ◽  
Ali M. Sayfy
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Spline Collocation ◽  
Extended System ◽  
Collocation Approach ◽  
Linear And Nonlinear

A cubic B-spline collocation approach is described and presented for the numerical solution of an extended system of linear and nonlinear second-order boundary-value problems. The system, whether regular or singularly perturbed, is tackled using a spline collocation approach constructed over uniform or non-uniform meshes. The rate of convergence is discussed theoretically and verified numerically to be of fourth-order. The efficiency and applicability of the technique are demonstrated by applying the scheme to a number of linear and nonlinear examples. The numerical solutions are contrasted with both analytical and other existing numerical solutions that exist in the literature. The numerical results demonstrate that this method is superior as it yields more accurate solutions.

scholarly journals An Algorithm: Optimal Homotopy Asymptotic Method for Solutions of Systems of Second-Order Boundary Value Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Rafiq Mufti ◽  
Muhammad Imran Qureshi ◽  
Salem Alkhalaf ◽  
S. Iqbal
Keyword(s):  
Exact Solutions ◽  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Small Perturbations ◽  
Forcing Function ◽  
Optimal Homotopy Asymptotic Method ◽  
Linear And Nonlinear Systems

Optimal homotopy asymptotic method (OHAM) is proposed to solve linear and nonlinear systems of second-order boundary value problems. OHAM yields exact solutions in just single iteration depending upon the choice of selecting some part of or complete forcing function. Otherwise, it delivers numerical solutions in excellent agreement with exact solutions. Moreover, this procedure does not entail any discretization, linearization, or small perturbations and therefore reduces the computations a lot. Some examples are presented to establish the strength and applicability of this method. The results reveal that the method is very effective, straightforward, and simple to handle systems of boundary value problems.

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