Absolute stability of an implicit method based on third-order off-step discretization for the initial-value problem on a graded mesh

2019 ◽  
Author(s):  
R. K. Mohanty ◽  
Bishnu Pada Ghosh
Keyword(s):  
Initial Value Problem ◽  
Absolute Stability ◽  
Implicit Method ◽  
Initial Value ◽  
Third Order ◽  
Graded Mesh

scholarly journals Solution Analysis of A 3rd Order Initial Value Problem

2019 ◽  
Vol 8 (2) ◽  
pp. 3784-3789 ◽  
Keyword(s):  
Exact Solution ◽  
Initial Value Problem ◽  
Absolute Stability ◽  
Numerical Differentiation ◽  
Initial Value ◽  
Step Method ◽  
Third Order ◽  
Transform Method ◽  
Differential Transform ◽  
Index Terms

In this article, we have used DT Method (Differential Transform Method) and Numerical Differentiation Method to solve a third order initial value problem . We observed that the solutions by these methods are very close to the exact solution. The methods have been demonstrated and hence the superiority of the ND Method is observed. A numerical example is illustrated by using DT and ND methods and the results were compared with exact solution. Index Terms : DT Method, Absolute stability, Multi-Step method, Numerical Differentiation

scholarly journals Geometric Properties Solutions of a Class of Third-Order Linear Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Afaf Ali Abubaker ◽  
Maslina Darus
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Linear Differential Equations ◽  
Open Unit ◽  
Open Unit Disk ◽  
Initial Value ◽  
Third Order ◽  
Geometric Properties ◽  
Order Linear ◽  
Linear Differential

We aim at investigating the geometric properties of the solutions of the initial-value problem which involves the following third-order linear differential equations: ω′′′(z)+Q(z)ω′(z)=0, ω(0)=0, ω′(0)=1, ω′′(0)=0, where Q(z) is analytic in the open unit disk U.

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