scholarly journals Fuzzy approximate solutions of second-order fuzzy linear boundary value problems

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang ◽  
Xiaoquan Lu
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Second Order ◽  
Linear Boundary

scholarly journals A Neuro-Swarming Intelligence-Based Computing for Second Order Singular Periodic Non-linear Boundary Value Problems

2020 ◽  
Vol 8 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Muhammad Asif Zahoor Raja ◽  
Juan L. G. Guirao ◽  
Muhammad Shoaib
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Linear Boundary ◽  
Non Linear

scholarly journals Three-Step Block Method for Solving Nonlinear Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Phang Pei See ◽  
Zanariah Abdul Majid ◽  
Mohamed Suleiman
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Second Order ◽  
Multiple Shooting ◽  
Variable Step Size ◽  
Nonlinear Boundary Value Problems ◽  
Block Method ◽  
Step Size ◽  
Multiple Shooting Techniques

We propose a three-step block method of Adam’s type to solve nonlinear second-order two-point boundary value problems of Dirichlet type and Neumann type directly. We also extend this method to solve the system of second-order boundary value problems which have the same or different two boundary conditions. The method will be implemented in predictor corrector mode and obtain the approximate solutions at three points simultaneously using variable step size strategy. The proposed block method will be adapted with multiple shooting techniques via the three-step iterative method. The boundary value problem will be solved without reducing to first-order equations. The numerical results are presented to demonstrate the effectiveness of the proposed method.

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

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