Numerical Solutions of Boundary Value Problems with So-Called Shooting Method

2021 ◽  
Author(s):  
Sujaul Chowdhury ◽  
Mubin Md. Al Furkan ◽  
Nazmus Sayadat Ifat
Keyword(s):  
Boundary Value Problems ◽  
Shooting Method ◽  
Numerical Solutions ◽  
Boundary Value

scholarly journals Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Suheel Abdullah Malik ◽  
Ijaz Mansoor Qureshi ◽  
Muhammad Amir ◽  
Ihsanul Haq
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Fitness Function ◽  
Boundary Value ◽  
Computational Technique ◽  
Singular Boundary ◽  
Interior Point Algorithm ◽  
Singular Boundary Value Problems ◽  
Hybrid Heuristic

We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

A Reliable Treatment for Solving Nonlinear Two-Point Boundary Value Problems

2007 ◽  
Vol 62 (9) ◽  
pp. 483-489
Author(s):  
Mustafa Inc
Keyword(s):  
Boundary Value Problems ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Shooting Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Point Boundary ◽  
Adomian Decomposition

In this paper, we study the modified decomposition method (MDM) for solving nonlinear twopoint boundary value problems (BVPs) and show numerical experiments. The modified form of the Adomian decomposition method which is more fast and accurate than the standard decomposition method (SDM) was introduced by Wazwaz. In addition, we will compare the performance of the MDM and the new nonlinear shooting method applied to the solutions of nonlinear two-point BVPs. The comparison shows that the MDM is reliable, efficient and easy for solving the nonlinear twopoint BVPs.

Increasing the Solution Accuracy in the Numerical Modeling of Boundary Value Problems Using Finite Element Method Based on Hankel Shape Functions

2019 ◽  
Vol 11 (07) ◽  
pp. 1950062
Author(s):  
S. Farmani ◽  
M. Ghaeini-Hessaroeyeh ◽  
S. Hamzehei-Javaran
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Element Approach ◽  
Solution Accuracy ◽  
Element Method

A new finite element approach is developed here for the modeling of boundary value problems. In the present model, the finite element method (FEM) is reformulated by new shape functions called spherical Hankel shape functions. The mentioned functions are derived from the first and second kind of Bessel functions that have the properties of both of them. These features provide an improvement in the solution accuracy with number of elements which are equal or lower than the ones used by the classic FEM. The efficiency and accuracy of the suggested model in the potential problems are examined by several numerical examples. Then, the obtained results are compared with the analytical and numerical solutions. The comparisons indicate the high accuracy of the present method.

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