Sufficient conditions for the convergence of the Magnus expansion

نویسنده

  • Fernando Casas
چکیده

Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equation Y ′ = A(t)Y . The first one provides a bound on the convergence domain based on the norm of the operator A(t). The second condition links the convergence of the expansion with the structure of the spectrum of Y (t), thus yielding a more precise characterization. Several examples are proposed to illustrate the main issues involved and the information on the convergence domain provided by both conditions.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Convergence, Consistency and Stability in Fuzzy Differential Equations

In this paper, we consider First-order fuzzy differential equations with initial value conditions. The convergence, consistency and stability of difference method for approximating the solution of fuzzy differential equations involving generalized H-differentiability, are studied. Then the local truncation error is defined and sufficient conditions for convergence, consistency and stability of ...

متن کامل

Favorable Plug Shape of an Aerospike Nozzle in Design, Over and Under Expansion Conditions

The influence of the plug shape on the performance of an aerospike nozzle thrust force is studied in different back pressure conditions. To generate smooth plug contours, Cubic B-Spline technique is employed. In the current research, basis functions are obtained using Deboor’s relation. The flow field around the aerospike nozzle is investigated implementing various shapes and the best of the ge...

متن کامل

Convergence of product integration method applied for numerical solution of linear weakly singular Volterra systems

We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

متن کامل

Convergence of a semi-analytical method on the fuzzy linear systems

In this paper, we apply the  homotopy analysis method (HAM) for solving fuzzy  linear systems and present  the necessary and sufficient conditions for the convergence of series solution obtained via the HAM. Also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the HAM is applied to linear system of equations. Comparisons are made between the ...

متن کامل

Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007