Computable a Posteriori $L_\infty $-Error Bounds for the Approximate Solution of Two-Point Boundary Value Problems

1975 ◽  
Vol 12 (6) ◽  
pp. 919-937 ◽  
Author(s):  
Mary Anne McCarthy ◽  
R. A. Tapia
Keyword(s):  
Approximate Solution ◽  
Boundary Value Problems ◽  
Error Bounds ◽  
Boundary Value ◽  
Point Boundary ◽  
A Posteriori

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.

The Modified VIM for Certain Type of the Nonlinear Two-Point Boundary Value Problems

2019 ◽  
Vol 17 (03) ◽  
pp. 1850131 ◽  
Author(s):  
Asghar Ghorbani ◽  
Hadi Passandideh
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problems ◽  
Convergence Analysis ◽  
Error Bounds ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Current Paper ◽  
Effective Procedure ◽  
Point Boundary

In the current paper, we introduce a different version of the variational iteration method (VIM) that provide an easy and effective procedure for solving nonlinear two-point boundary-value problems appearing in applied and engineering applications. For problems where convergence rate of the original VIM is slow, the method can be readily improved to increase convergence rate. Convergence analysis and error bounds are discussed. Finally, applicability of the proposed method and accuracy are examined by solving three problems.

scholarly journals Existence of an approximate solution for a class of fractional multi-point boundary value problems with the derivative term

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yanbin Sang ◽  
Luxuan He
Keyword(s):  
Fixed Point ◽  
Approximate Solution ◽  
Boundary Value Problems ◽  
Unique Solution ◽  
Fixed Point Theorems ◽  
Nonlinear Operator ◽  
Boundary Value ◽  
Point Boundary ◽  
Derivative Term ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems to have a unique solution, and we construct the corresponding iterative sequences to approximate the unique solution.

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