Uniformly convergent non-standard finite difference methods for singularly perturbed differential-difference equations with delay and advance

2006 ◽  
Vol 66 (2) ◽  
pp. 272-296 ◽  
Author(s):  
Kailash C. Patidar ◽  
Kapil K. Sharma
Keyword(s):  
Finite Difference ◽  
Difference Equations ◽  
Finite Difference Methods ◽  
Singularly Perturbed ◽  
Uniformly Convergent ◽  
Difference Methods ◽  
Equations With Delay

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.

Fast Algorithm for the Inverse Matrices of Periodic Adding Element Tridiagonal Matrices

2010 ◽  
Vol 159 ◽  
pp. 464-468
Author(s):  
Hong Ling Fan
Keyword(s):  
Finite Difference ◽  
Boundary Value Problems ◽  
Linear Systems ◽  
Difference Equations ◽  
Fast Algorithm ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Triangular Factorization ◽  
Tridiagonal Matrices ◽  
Difference Methods

Adding element tridiagonal periodic matrices have an important effect for the algorithms of solving linear systems，computing the inverses, the triangular factorization，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.

scholarly journals Non-standard numerical scheme for singularly perturbed parabolic partial differential equation with long time lag arising in control theory

2021 ◽  
Author(s):  
NAOL NEGERO ◽  
Gemechis Duressa
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Finite Difference Methods ◽  
Time Lag ◽  
Singularly Perturbed ◽  
Parabolic Partial Differential Equation ◽  
Long Time ◽  
Difference Methods ◽  
Two Parameters

For the numerical solution of singularly perturbed second-order parabolic partial differential equation of one dimensional convection-diffusion type with long time delays arising in control theory, a novel class of fitted operator finite difference methods is constructed using non-standard finite difference methods. Since the two parameters; time lag and perturbation parameters are sources for the simultaneous occurrence of time-consuming and high speed phenomena of the physical systems that depends on the present and past history, our study here is to capture the effect of the two parameters on the boundary layer. The spatial derivative is suitably replaced by a difference operator followed by the time derivative is replaced by the Crank-Nicolson based scheme. A second-order parameter-uniform error bounds are established to provide numerical results.

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