scholarly journals Centroidal-Polygon: Solving First Order Ordinary Differential Equation using Centroidal mean to improve Euler Method

2021 ◽  
Vol 1874 (1) ◽  
pp. 012038
Author(s):  
Z Nur Shahirah ◽  
S Nooraida ◽  
W A Wan Farah Hanan ◽  
R A Suzanna ◽  
M A Iliana
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Euler Method ◽  
Order Ordinary Differential Equation ◽  
First Order

DERIVATION OF 2-POINT ZERO STABLENUMERICAL ALGORITHM OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 5 (2) ◽  
pp. 579-583
Author(s):  
Muhammad Abdullahi ◽  
Bashir Sule ◽  
Mustapha Isyaku
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Order Ordinary Differential Equation ◽  
Differentiation Formula ◽  
First Order ◽  
Backward Differentiation Formula

This paper is aimed at deriving a 2-point zero stable numerical algorithm of block backward differentiation formula using Taylor series expansion, for solving first order ordinary differential equation. The order and zero stability of the method are investigated and the derived method is found to be zero stable and of order 3. Hence, the method is suitable for solving first order ordinary differential equation. Implementation of the method has been considered

scholarly journals Generalized (ψ,α,β)—Weak Contractions for Initial Value Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 266 ◽  
Author(s):  
Piyachat Borisut ◽  
Poom Kumam ◽  
Vishal Gupta ◽  
Naveen Mani
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problems ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Initial Value ◽  
Order Ordinary Differential Equation ◽  
Ordered Metric Spaces ◽  
First Order

A class of generalized ( ψ , α , β ) —weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation to find its solution.

scholarly journals Fixed Point of Orthogonal F-Suzuki Contraction Mapping on O-Complete b-Metric Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ismat Beg ◽  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fixed Point ◽  
Unique Solution ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Generalized Orthogonal

In this paper, we introduce the concept of generalized orthogonal F -Suzuki contraction mapping and prove some fixed point theorems on orthogonal b -metric spaces. Our results generalize and extend some of the well-known results in the existing literature. As an application of our results, we show the existence of a unique solution of the first-order ordinary differential equation.

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