Application of interval analysis techniques to linear systems. II. The interval matrix exponential function

1988 ◽  
Vol 35 (10) ◽  
pp. 1230-1242 ◽  
Author(s):  
E.P. Oppenheimer
Keyword(s):  
Linear Systems ◽  
Exponential Function ◽  
Interval Analysis ◽  
Matrix Exponential ◽  
Interval Matrix ◽  
Analysis Techniques ◽  
Matrix Exponential Function

Application of Interval Analysis Techniques to Linear Systems

1987 ◽  
Vol 20 (5) ◽  
pp. 251-256
Author(s):  
A.N. Michel ◽  
E.P. Oppenheimer
Keyword(s):  
Linear Systems ◽  
Interval Analysis ◽  
Analysis Techniques

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.

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