Upwind and midpoint upwind difference methods for time-dependent differential difference equations with layer behavior

2008 ◽  
Vol 202 (2) ◽  
pp. 453-471 ◽  
Author(s):  
V.P. Ramesh ◽  
M.K. Kadalbajoo
Keyword(s):  
Difference Equations ◽  
Time Dependent ◽  
Difference Methods ◽  
Layer Behavior

The solution of an infinite set of differential-difference equations occurring in polymerization and queueing problems

1963 ◽  
Vol 59 (1) ◽  
pp. 117-124 ◽  
Author(s):  
A. Wragg
Keyword(s):  
Difference Equations ◽  
Queueing Theory ◽  
Bessel Functions ◽  
Formal Solution ◽  
Monomer Concentration ◽  
Arrival Rate ◽  
Time Dependent ◽  
Type Integral ◽  
Dependent Parameter ◽  
Infinite Set

AbstractThe time-dependent solutions of an infinite set of differential-difference equations arising from queueing theory and models of ‘living’ polymer are expressed in terms of modified Bessel functions. Explicit solutions are available for constant values of a parameter describing the arrival rate or monomer concentration; for time-dependent parameter a formal solution is obtained in terms of a function which satisfies a Volterra type integral equation of the second kind. These results are used as the basis of a numerical method of solving the infinite set of differential equations when the time-dependent parameter itself satisfies a differential equation.

scholarly journals On time dependent multistep dynamic processes

1991 ◽  
Vol 43 (1) ◽  
pp. 51-61
Author(s):  
Ferenc Szidarovszky ◽  
Ioannis K. Argyros
Keyword(s):  
Topological Space ◽  
Discrete Time ◽  
Difference Equations ◽  
Time Scale ◽  
Time Dependent ◽  
Dynamic Processes ◽  
Monotone Convergence ◽  
Speed Of Convergence ◽  
Nonlinear Difference Equations ◽  
Ordered Topological Space

The discrete time scale Liapunov theory is extended to time dependent, higher order, nonlinear difference equations in a partially ordered topological space. The monotone convergence of the solution is examined and the speed of convergence is estimated.

Fast Algorithm for the Inverse Matrices of Adding Element Tridiagonal Periodic Matrices in Signal Processing

2010 ◽  
Vol 121-122 ◽  
pp. 682-686
Author(s):  
Yan Lei Zhao ◽  
Xue Ting Liu
Keyword(s):  
Signal Processing ◽  
Finite Difference ◽  
Boundary Value Problems ◽  
Difference Equations ◽  
Fast Algorithm ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Practical Applications ◽  
Tridiagonal Matrices ◽  
Difference Methods

Adding element tridiagonal matrices play a very important role in the theory and practical applications, such as the boundary value problems by finite difference methods, interpolation by cubic splines, three-term difference equations and so on. In this paper, we give a fast algorithm for the Inverse Matrices of periodic adding element tridiagonal matrices.

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