An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation

1999 ◽  
pp. 289-310 ◽  
Author(s):  
Nedialko S. Nedialkov ◽  
Kenneth R. Jackson
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problem ◽  
Initial Value ◽  
Rigorous Bounds ◽  
Bounds On The Solution

The ODE- and BVP-Solvers With M&T Applications

2021 ◽  
pp. 166-190
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problems ◽  
Initial Value Problem ◽  
Hydrodynamic Lubrication ◽  
Boundary Value ◽  
Final Part ◽  
Sliding Surface ◽  
Initial Value ◽  
Mass System

The chapter introduces solvers for solving initial and boundary value problems (IVP&BVP) of the ordinary differential equation (ODE). It begins with a description of the ODE solver commands applied to the initial value problem and presents the steps for solving the actual ODE. Further, the chapter presents the BVP-solver commands and steps for their usage. The solutions are presented through real examples. In the final part, the studied ODE and BVP commands are applied, mainly to problems oriented for mechanics and tribology (M&T). At the end of the chapter, applications to the M&T problems are presented; they illustrate how to solve IVP for the spring-mass system and particle falling, as well as BVP for a single clamped beam and hydrodynamic lubrication of a sliding surface covered with semicircular pores.

scholarly journals Solution of Ordinary Differential Equation Using Green's Function & Sturm - Liouville Problem

2019 ◽  
pp. 241-244
Author(s):  
S. Angel Auxzaline Mary ◽  
T. Ramesh
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Initial Value Problem ◽  
Series Representation ◽  
Liouville Problem ◽  
Initial Value ◽  
Sturm Liouville

In this paper, we describe Green's function to determine the importance of this function, i.e. Boundary & Initial Value problem, Sturm-Liouville Problem. Along with the series representation of Green's Function.

scholarly journals SEMIGROUP-LIKE PROPERTY OF MITTAG-LEFFLER FUNCTION

2016 ◽  
Vol 8 (1) ◽  
pp. 21
Author(s):  
Bambang Hendriya Guswanto
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Caputo Fractional Derivative ◽  
Initial Value

In this article, we discuss the semigroup-like property of Mittag-Leffler function which is used to solve the initial value problem of an ordinary differential equation involving Caputo fractional derivative.

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