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 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.

Three-Dimensional Boundary Value Problems of Elastothermodiffusion with Mixed Boundary Conditions

1997 ◽  
Vol 4 (3) ◽  
pp. 243-258
Author(s):  
T. Burchuladze ◽  
Yu. Bezhuashvili
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Singular Integrals ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Mixed Boundary Conditions ◽  
Theory Of Elasticity ◽  
Classical Solutions

Abstract We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [Kupradze, Gegelia, Basheleishvili, and Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity, North-Holland Publishing Company, 1979, Russian original, 1976–Mikhlin, Multi-dimensional singular integrals and integral equations, 1962], we prove theorems on the existence and uniqueness of the classical solutions of these problems.

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