Cyclic finite-difference methods for ordinary differential equations

1974 ◽  
pp. 134-143 ◽  
Author(s):  
Hans J. Stetter
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Finite Difference Methods ◽  
Difference Methods

scholarly journals Comparison between standard and non-standard finite difference methods for solving first and second order ordinary differential equations

2015 ◽  
Vol 4 (2) ◽  
pp. 316
Author(s):  
Abdulrahman Yaghoubi ◽  
Hashem Saberi Najafi
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Finite Difference Methods ◽  
Second Order ◽  
Difference Methods

<p>In this paper, we solve some first and second order ordinary differential equations by the standard and non-standard finite difference methods and compare results of these methods. Illustrative examples have been provided, and the results of two methods compared with the exact solutions.</p>

scholarly journals A Step Block Algorithm for Solving First Order Initial Value Problems in Ordinary Differential Equations

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Emmanuel O Adeyefa ◽  
Oluwatosin Fadaka
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Finite Difference Methods ◽  
Initial Value ◽  
Step Method ◽  
Block Algorithm ◽  
One Step ◽  
Difference Methods

The implementation of the newly formulated polynomials, ADEM-B orthogonal polynomials,  valid in the interval [-1, 1] with respect to weight function is our major focus in this work. The polynomials, which serve as basis function are employed to develop finite difference methods. Varying off-step points are considered for only One-Step method for the solution of the initial value problems of Ordinary Differential Equations (ODEs).  By selection of points for both interpolation and collocation, threeimportant class of block finite difference methods are produced. The methods are analyzed for their basic properties and findings show that they are accurate and convergent.

scholarly journals A Finite Difference Fictitious Domain Wavelet Method for Solving Dirichlet Boundary Value Problem

2021 ◽  
Vol 14 (3) ◽  
pp. 706-722
Author(s):  
Francis Ohene Boateng ◽  
Joseph Ackora-Prah ◽  
Benedict Barnes ◽  
John Amoah-Mensah
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Finite Difference Methods ◽  
Dirichlet Boundary Conditions ◽  
Fictitious Domain ◽  
Dirichlet Boundary Value Problem ◽  
Wavelet Method ◽  
Difference Methods

In this paper, we introduce a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) for solving two dimensional (2D) linear elliptic  partial differential equations (PDEs) with Dirichlet boundary conditions on regular geometric domain. The method reduces the 2D PDE into a 1D system of ordinary differential equations and applies a compactly supported wavelet to approximate the solution. The problem is embedded in a fictitious domain to aid the enforcement of the Dirichlet boundary conditions. We present numerical analysis and show that our method yields better approximation to the solution of the Dirichlet problem than traditional methods like the finite element and finite difference methods.

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