scholarly journals ON THE SOLUTION OF TWO POINT BOUNDARY VALUE PROBLEMS WITH TWO POINT DIRECT METHOD

2012 ◽  
Vol 09 ◽  
pp. 566-573 ◽  
Author(s):  
PEI SEE PHANG ◽  
ZANARIAH ABDUL MAJID ◽  
MOHAMED SULEIMAN
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Boundary Value Problems ◽  
Simple Form ◽  
Direct Method ◽  
Boundary Value ◽  
Numerical Results ◽  
Point Boundary ◽  
Step Size ◽  
Shooting Technique

The two point boundary value problems (BVPs) occur in a wide variety of applications especially in sciences such as chemistry and biology. In this paper, we propose two point direct method of order six for solving nonlinear two point boundary value problems directly. This method is presented in a simple form of Adams Mouton type and determines the approximate solution at two point simultaneously. The method will be implemented using constant step size via shooting technique adapted with three-step iterative method. Numerical results are given to compare the efficiency of the proposed method with the Runge-Kutta and bvp4c method.

scholarly journals Direct Integration of Boundary Value Problems Using the Block Method via the Shooting Technique Combined with Steffensen’s Strategy

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1075 ◽  
Author(s):  
Nadirah Mohd Nasir ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail ◽  
Norfifah Bachok
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Direct Method ◽  
Boundary Value ◽  
Mixed Boundary Conditions ◽  
Direct Integration ◽  
Step Size ◽  
Time Saving ◽  
Shooting Technique

This study is intended to evaluate numerically the solution of second order boundary value problems (BVPs) subject to mixed boundary conditions using a direct method. The mixed set of boundary conditions is subsumed under Type 1: mixed boundary conditions of Dirichlet and Robin and Type 2: mixed boundary conditions of Robin and Neumann. The direct integration procedure will compute the solutions at two values concurrently within a block with a fixed step size. The shooting technique adapted to the derivative free Steffensen method is employed as the iterative strategy to generate the new initial estimates. Four numerical examples are given to measure the efficiency and effectiveness of the developed numerical scheme of order six. The computational comparison indicates that the proposed method gives favorably competitive performance compared to the existing method in terms of accuracy, total function calls, and time saving.

scholarly journals A New Numerical Algorithm for Two-Point Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Lihua Guo ◽  
Boying Wu ◽  
Dazhi Zhang
Keyword(s):  
Exact Solution ◽  
Error Analysis ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Numerical Algorithm ◽  
Numerical Stability ◽  
Boundary Value ◽  
Numerical Results ◽  
Point Boundary ◽  
Stability And Error Analysis

We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that then-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.

Sign in / Sign up

Export Citation Format

Share Document