scholarly journals A Seven-Step Block Multistep Method for the Solution of First Order Stiff Differential Equations

2020 ◽  
Vol 12 (1) ◽  
pp. 72-82
Author(s):  
Solomon Gebregiorgis ◽  
Hailu Muleta
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Power Series ◽  
Differential Equations ◽  
Multistep Method ◽  
Stiff Differential Equations ◽  
Block Method ◽  
Initial Value ◽  
Numerical Examples ◽  
First Order

In this paper, a seven-step block method for the solution of first order initial value problem in ordinary differential equations based on collocation of the differential equation and interpolation of the approximate solution using power series have been formed. The method is found to be consistent and zero-stable which guarantees convergence. Finally, numerical examples are presented to illustrate the accuracy and effectiveness of the method.  Keywords: Power series, Collocation, Interpolation, Block method, Stiff.

scholarly journals FORMULATION OF BLOCK SCHEMES WITH LINEAR MULTISTEP METHOD FOR THE APPROXIMATION OF FIRST-ORDER IVPS

2020 ◽  
Vol 4 (3) ◽  
pp. 313-322
Author(s):  
Sunday Obomeviekome Imoni ◽  
D. I. Lanlege ◽  
E. M. Atteh ◽  
J. O. Ogbondeminu
Keyword(s):  
Basis Function ◽  
Initial Value Problems ◽  
Hermite Polynomials ◽  
Multistep Method ◽  
Linear Multistep Method ◽  
Initial Value ◽  
Numerical Examples ◽  
First Order ◽  
Block Scheme ◽  
Multi Step Methods

ABSTRACT In this paper, formulation of an efficient numerical schemes for the approximation first-order initial value problems (IVPs) of ordinary differential equations (ODE) is presented. The method is a block scheme for some k-step linear multi-step methods (and) using the Hermite Polynomials a basis function. The continuous and discrete linear multi-step methods (LMM) are formulated through the technique of collocation and interpolation. Numerical examples of ODE have been examined and results obtained show that the proposed scheme can be efficient in solving initial value problems of first order ODE.

scholarly journals Solving Fuzzy Differential Equations by Using Power Series

2020 ◽  
pp. 92-107
Author(s):  
Rasha H. Ibraheem
Keyword(s):  
Approximate Solution ◽  
Power Series ◽  
Differential Equations ◽  
Taylor Expansion ◽  
Series Solution ◽  
Convergent Series ◽  
Initial Value ◽  
Third Order ◽  
Technical Accuracy ◽  
Made In

In this paper, the series solution is applied to solve third order fuzzy differential equations with a fuzzy initial value. The proposed method applies Taylor expansion in solving the system and the approximate solution of the problem which is calculated in the form of a rapid convergent series; some definitions and theorems are reviewed as a basis in solving fuzzy differential equations. An example is applied to illustrate the proposed technical accuracy. Also, a comparison between the obtained results is made, in addition to the application of the crisp solution, when the-level equals one.

scholarly journals An Efficient Zero-Stable Numerical Method for Fourth-Order Differential Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
S. J. Kayode
Keyword(s):  
Approximate Solution ◽  
Power Series ◽  
Differential Equations ◽  
Numerical Method ◽  
Fourth Order ◽  
Optimal Order ◽  
Direct Solution ◽  
Order Of Accuracy ◽  
First Order ◽  
Stable Numerical Method

The purpose of this paper is to produce an efficient zero-stable numerical method with the same order of accuracy as that of the main starting values (predictors) for direct solution of fourth-order differential equations without reducing it to a system of first-order equations. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is consistent, symmetric, and of optimal order . The main predictor for the method is also consistent, symmetric, zero-stable, and of optimal order .

scholarly journals Four-Step One Hybrid Block Methods for Solution of Fourth Derivative Ordinary Differential Equations

2021 ◽  
pp. 1-10
Author(s):  
Raymond, Dominic ◽  
Skwame, Yusuf ◽  
Adiku, Lydia
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Multistep Method ◽  
Linear Multistep Method ◽  
Block Method ◽  
Step Method ◽  
Block Methods ◽  
Fourth Derivative ◽  
Continuous Block

We consider developing a four-step one offgrid block hybrid method for the solution of fourth derivative Ordinary Differential Equations. Method of interpolation and collocation of power series approximate solution was used as the basis function to generate the continuous hybrid linear multistep method, which was then evaluated at non-interpolating points to give a continuous block method. The discrete block method was recovered when the continuous block was evaluated at all step points. The basic properties of the methods were investigated and said to be converge. The developed four-step method is applied to solve fourth derivative problems of ordinary differential equations from the numerical results obtained; it is observed that the developed method gives better approximation than the existing method compared with.

scholarly journals Computation of First order Delay Differential Equations via Simpson Block Method

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Ridwanulahi I Abdulganiy ◽  
Olusheye A Akinfenwa ◽  
Osaretin E Enobabor ◽  
Blessing I Orji ◽  
Solomon A Okunuga
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Step Width ◽  
Block Method ◽  
Delay Term ◽  
First Order ◽  
Collocation Technique ◽  
Delay Differential

A family of Simpson Block Method (SBM) is proposed for the numerical integration of Delay Differential Equations (DDEs). The methods are developed through multistep collocation technique using constant step width. The convergence and accuracy of the methods are established through some standard DDEs in the reviewed literature. Keywords— Block Method, Collocation Technique, Delay Term, Delay Differential Equation, Self Starting.   

scholarly journals APPROXIMATE SOLUTION OF A NONLINEAR INTEGRO-DIFFERENTIAL EQUATION BY THE NEWTON-KANTOROVICH METHOD

2020 ◽  
pp. 609-614
Author(s):  
I.A. Usenov ◽  
Yu.V. Kostyreva ◽  
S. Almambet kyzy
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Approximate Solution ◽  
Initial Value Problem ◽  
Nonlinear Integral Equation ◽  
Initial Problem ◽  
Initial Value ◽  
Kantorovich Method ◽  
Integro Differential Equation ◽  
First Order

In this paper, we propose a method for studying the initial value problem for a first-order nonlinear integro-differential equation. The initial problem is reduced by substitution to a nonlinear integral equation with the Urson operator. To construct a solution to a nonlinear integral equation, the Newton-Kantorovich method is used.

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