Matrix-Variation-of-Constants Formula

2015 ◽  
pp. 1-21 ◽  
Author(s):  
Xinyuan Wu ◽  
Kai Liu ◽  
Wei Shi
Keyword(s):  
Variation Of Constants Formula ◽  
Variation Of Constants

scholarly journals Decomposition and Variation-of-Constants Formula in the Phase Space for Integral Equations

2012 ◽  
Vol 55 (3) ◽  
pp. 479-520 ◽  
Author(s):  
Hideaki Matsunaga ◽  
Satoru Murakami ◽  
Van Minh Nguyen
Keyword(s):  
Phase Space ◽  
Integral Equations ◽  
Variation Of Constants Formula ◽  
Variation Of Constants

scholarly journals Truncated V-fractional Taylor's Formula with Applications

2018 ◽  
Vol 19 (3) ◽  
pp. 525
Author(s):  
José Vanterler da Costa Sousa ◽  
Edmundo Capelas de Oliveira
Keyword(s):  
Fractional Integral ◽  
Taylor’S Formula ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Schwartz Inequality ◽  
Taylor's Formula

In this paper, we present and prove a new truncated V-fractional Taylor's formula using the truncated V-fractional variation of constants formula. In this sense, we present the truncated V-fractional Taylor's remainder by means of V-fractional integral, essential for analyzing and comparing the error, when approaching functions by polynomials. From these new results, some applications were made involving some inequalities, specifically, we generalize the Cauchy-Schwartz inequality.

scholarly journals Numerical discretization of stochastic oscillators with generalized numerical integrators

2021 ◽  
Vol 25 (Spec. issue 1) ◽  
pp. 65-75
Author(s):  
Ali Sirma ◽  
Resat Kosker ◽  
Muzaffer Akat
Keyword(s):  
Numerical Experiments ◽  
Numerical Scheme ◽  
Additive Noise ◽  
First Order ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Numerical Integrators ◽  
One Step ◽  
Numerical Discretization ◽  
Stochastic Oscillators

In this study, we propose a numerical scheme for stochastic oscillators with additive noise obtained by the method of variation of constants formula using generalized numerical integrators. For both of the displacement and the velocity components, we show that the scheme has an order of 3/2 in one step convergence and a first order in overall convergence. Theoretical statements are supported by numerical experiments.

scholarly journals Variation of constants formula and exponential dichotomy for nonautonomous non-densely defined Cauchy problems

2020 ◽  
pp. 1-43
Author(s):  
Pierre Magal ◽  
Ousmane Seydi
Keyword(s):  
Exponential Dichotomy ◽  
Homogeneous Problem ◽  
Cauchy Problems ◽  
Small Perturbations ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Age Structured ◽  
Necessary And Sufficient ◽  
Age Structured Model ◽  
Densely Defined

Abstract In this paper, we extend to the non-Hille–Yosida case a variation of constants formula for a nonautonomous and nonhomogeneous Cauchy problems first obtained by Gühring and Räbiger. By using this variation of constants formula, we derive a necessary and sufficient condition for the existence of an exponential dichotomy for the evolution family generated by the associated nonautonomous homogeneous problem. We also prove a persistence result of the exponential dichotomy for small perturbations. Finally, we illustrate our results by considering two examples. The first example is a parabolic equation with nonlocal and nonautonomous boundary conditions, and the second example is an age-structured model that is a hyperbolic equation.

Sign in / Sign up

Export Citation Format

Share Document