New Algorithm of Two-Point Block Method for Solving Boundary Value Problem with Dirichlet and Neumann Boundary Conditions

Pei See Phang; Zanariah Abdul Majid; Fudziah Ismail; Khairil Iskandar Othman; Mohamed Suleiman

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New Algorithm of Two-Point Block Method for Solving Boundary Value Problem with Dirichlet and Neumann Boundary Conditions

机译：求解Dirichlet和Neumann边界条件的边值问题的两点分块新算法

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Two-point block method with variable step-size strategy is presented to obtain the solutions for boundary value problems directly. Dirichlet type and Neumann type of boundary conditions are studied in this paper. Multiple shooting techniques adapted with the three-step iterative method are employed for generating the guessing value. Six boundary value problems are solved using the proposed method, and the numerical results are compared to the existing methods. The results suggest a significant improvement in the efficiency of the proposed methods in terms of the number of steps, execution time, and accuracy.

机译：提出了变步长策略的两点分块方法，直接获得了边值问题的解。本文研究了边界条件的Dirichlet型和Neumann型。采用与三步迭代方法相适应的多种拍摄技术来生成猜测值。使用所提出的方法解决了六个边值问题，并将数值结果与现有方法进行了比较。结果表明，在步骤数，执行时间和准确性方面，所提出方法的效率有了显着提高。

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来源
《Mathematical Problems in Engineering》 |2013年第3期|917589.1-917589.10|共10页
作者
Pei See Phang; Zanariah Abdul Majid; Fudziah Ismail; Khairil Iskandar Othman; Mohamed Suleiman;
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Department of Mathematics, Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia;

Department of Mathematics, Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia,Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia;

Department of Mathematics, Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia,Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia;

Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia;

Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, 43400 Serdang, Malaysia;

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1. New Algorithm of Two-Point Block Method for Solving Boundary Value Problem with Dirichlet and Neumann Boundary Conditions [J] . Pei SeePhang, ZanariahAbdul Majid, FudziahIsmail, Mathematical Problems in Engineering: Theory, Methods and Applications . 2013,第1期

机译：求解Dirichlet和Neumann边界条件边值问题的两点分块新算法
2. Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions [J] . Emad H. Aly, Abdelhalim Ebaid, Randolph Rach Computers & mathematics with applications . 2012,第6期

机译：用Neumann边界条件求解两点非线性边值问题的Adomian分解方法的进展
3. Diagonal Block Method for Solving Two-Point Boundary Value Problems with Robin Boundary Conditions [J] . Nasir Nadirah Mohd, Majid Zanariah Abdul, Ismail Fudziah, Mathematical Problems in Engineering . 2018,第12期

机译：具有Robin边界条件的两点边值问题的对角线块法
4. A numerical algorithm for solving Laplace and Poisson type partial differential equations on a uniform rectangular mesh with Dirichlet and Neumann boundary conditions [C] . Vasos Pavlika WSEAS International Conferences . 2008

机译：用Dirichlet和Neumann边界条件求解LAPLACH和泊松型偏微分方程的数值算法
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6. New algorithms for solving third- and fifth-order two point boundary value problems based on nonsymmetric generalized Jacobi Petrov–Galerkin method [O] . E.H. Doha, W.M. Abd-Elhameed, Y.H. Youssri 2015

机译：基于非对称广义Jacobi Petrov-Galerkin方法求解三阶和五阶两点边值问题的新算法
7. Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions [O] . Aly Emad H., Ebaid Abdelhalim, Rach Randolph 2012

机译：求解具有Neumann边界条件的两点非线性边值问题的Adomian分解方法的进展

New Algorithm of Two-Point Block Method for Solving Boundary Value Problem with Dirichlet and Neumann Boundary Conditions

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