Two-Step Hybrid Block Method for Solving First Order Ordinary Differential Equations Using Power Series Approach

2018 ◽  
Vol 28 (1) ◽  
pp. 1-7
Author(s):  
G Ajileye ◽  
S Amoo ◽  
O Ogwumu
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Block Method ◽  
First Order

An Order Four Block Method with Three Generalized Off Step Points for Solving First Order Ordinary Differential Equations

2016 ◽  
Vol 13 (10) ◽  
pp. 7574-7580
Author(s):  
Zurni Omar ◽  
Ra’ft Abdelrahim ◽  
John Olusola Kuboye
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Single Step ◽  
New Method ◽  
Block Method ◽  
First Order ◽  
Order Four

This paper presents a single-step block method with three generalized off-step points for solving first order ordinary differential equations. The approach employed in developing this new method is interpolating the approximated power series of order four at xn as well as at all off-step points and collocating the derivative of the power series at xn+1. The developed method is zero-stable, consistent, convergent and of order four. The new method has better accuracy than the existing methods when solving first order ordinary differential equations.

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 Modified Legendre Collocation Block Method for Solving Initial Value Problems of First Order Ordinary Differential Equations

OALib ◽  
2018 ◽  
Vol 05 (07) ◽  
pp. 1-15
Author(s):  
Toyin Gideon Okedayo ◽  
Ayodele Olakiitan Owolanke ◽  
Olaseni Taiwo Amumeji ◽  
Muyiwa Philip Adesuyi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Block Method ◽  
Initial Value ◽  
First Order

scholarly journals One–Step Hybrid Block Scheme for the Numerical Approximation for Solution of Third Order Initial Value Problems

2021 ◽  
pp. 51-61
Author(s):  
J. Sabo ◽  
T. Y. Kyagya ◽  
M. Solomon
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Block Method ◽  
Initial Value ◽  
Third Order ◽  
First Order ◽  
Block Algorithm ◽  
One Step ◽  
Linear Block

In this research, we have proposed the simulation of linear block algorithm for modeling third order highly stiff problem without reduction to a system of first order ordinary differential equation, to address the weaknesses in reduction method. The method is derived using the linear block method through interpolation and collocation. The basic properties of the block method were recovered and was found to be consistent, convergent and zero-stability. The new block method is been applied to model third order initial value problems of ordinary differential equations without reducing the equations to their equivalent systems of first order ordinary differential equations. The result obtained on the process on some sampled modeled third order linear problems give better approximation than the existing methods which we compared our result with.

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