scholarly journals Closed-Form Solutions of Linear Ordinary Differential Equations with General Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 226
Author(s):  
Efthimios Providas ◽  
Stefanos Zaoutsos ◽  
Ioannis Faraslis
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Closed Form ◽  
Linear Operators ◽  
General Boundary ◽  
Order Differential Operator ◽  
General Boundary Conditions ◽  
Symbolic Form ◽  
Closed Form Solutions

This paper deals with the solution of boundary value problems for ordinary differential equations with general boundary conditions. We obtain closed-form solutions in a symbolic form of problems with the general n-th order differential operator, as well as the composition of linear operators. The method is based on the theory of the extensions of linear operators in Banach spaces.

scholarly journals The Ornstein-Uhlenbeck-Type Model with a Hybrid Dividend Strategy

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Dan Zhu ◽  
Chuancun Yin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Closed Form ◽  
Generating Functions ◽  
Type Model ◽  
Value Functions ◽  
Closed Form Solutions ◽  
Time Value ◽  
Moment Generating Functions

We consider the Ornstein-Uhlenbeck-type model. We first introduce the model and then find the ordinary differential equations and boundary conditions satisfied by the dividend functions; closed-form solutions for the dividend value functions are given. We also study the distribution of the time value of ruin. Furthermore, the moments and moment-generating functions of total discounted dividends until ruin are discussed.

scholarly journals Riccati equations

1987 ◽  
Vol 10 (1) ◽  
pp. 205-207
Author(s):  
Lloyd K. Williams
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Closed Form ◽  
Riccati Equations ◽  
Second Order ◽  
Closed Form Solutions ◽  
The Matrix ◽  
Matrix Case

In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.

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