The Matrix Exponential Function and Systems of Differential Equations Using Derive

1995 ◽  
Vol 26 (2) ◽  
pp. 146
Author(s):  
Robert J. Hill ◽  
Mark S. Mazur
Keyword(s):  
Differential Equations ◽  
Exponential Function ◽  
Matrix Exponential ◽  
Systems Of Differential Equations ◽  
The Matrix ◽  
Matrix Exponential Function

scholarly journals On the numerical solution of the diffusion equation with a nonlocal boundary condition

2003 ◽  
Vol 2003 (2) ◽  
pp. 81-92 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Differential Equations ◽  
Diffusion Equation ◽  
Recurrence Relation ◽  
Exponential Function ◽  
Nonlocal Boundary ◽  
Matrix Exponential ◽  
Finite Difference Approximation ◽  
Partial Differential ◽  
First Order ◽  
Matrix Exponential Function

Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (MOL) semidiscretization approach is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations (ODEs). The partial derivative with respect to the space variable is approximated by a second-order finite-difference approximation. The solution of the resulting system of first-order ODEs satisfies a recurrence relation which involves a matrix exponential function. Numerical techniques are developed by approximating the exponential matrix function in this recurrence relation. We use a partial fraction expansion to compute the matrix exponential function via Pade approximations, which is particularly useful in parallel processing. The algorithm is tested on a model problem from the literature.

Numerical Range for the Matrix Exponential Function

2016 ◽  
Vol 31 ◽  
pp. 633-645
Author(s):  
Christos Chorianopoulos ◽  
Chun-Hua Guo
Keyword(s):  
Exponential Function ◽  
Numerical Range ◽  
Matrix Exponential ◽  
Topological Properties ◽  
The Matrix ◽  
Matrix Exponential Function ◽  
Square Matrix

For a given square matrix A, the numerical range for the exponential function e^(At), t in C, is considered. Some geometrical and topological properties of the numerical range are presented.

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