Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub-diffusion equations

2015 ◽  
Vol 22 (5) ◽  
pp. 866-882 ◽  
Author(s):  
Xin Lu ◽  
Hong-Kui Pang ◽  
Hai-Wei Sun
Keyword(s):  
Toeplitz Matrix ◽  
Diffusion Equations ◽  
Triangular Toeplitz Matrix

scholarly journals METODE ALTERNATIF DALAM MENENTUKAN SOLUSI PARTIKULAR PERSAMAAN EULER-CAUCHY

2021 ◽  
Vol 15 (1) ◽  
pp. 085-094
Author(s):  
Mariatul Kiftiah ◽  
Yudhi Yudhi ◽  
Alvi Yanitami
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Explicit Formula ◽  
Toeplitz Matrix ◽  
Variable Coefficients ◽  
Linear Ordinary Differential Equation ◽  
Cauchy Equation ◽  
Natural Logarithm ◽  
Particular Solution ◽  
Triangular Toeplitz Matrix

Euler-Cauchy equation is the typical example of a linear ordinary differential equation with variable coefficients. In this paper, we apply the alternative method to determine the particular solution of Euler-Cauchy nonhomogenous with polynomial and natural logarithm form. An explicit formula of the particular solution is derived from the use of an upper triangular Toeplitz matrix. The study showed that this method could be finding the particular solution for the Euler-Cauchy equation

Computer Simulation of Amperometric Biosensor Response to Mixtures of Compounds

2002 ◽  
Vol 7 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
J. Christensen ◽  
F. Ivanauskas ◽  
J. Kulys
Keyword(s):  
Computer Simulation ◽  
Enzymatic Reaction ◽  
Diffusion Equations ◽  
Response Data ◽  
Finite Difference Technique ◽  
Stationary Diffusion ◽  
Biosensor Array ◽  
Menten Kinetic ◽  
Biosensor Response

A mathematical model of amperometric biosensors has been developed. The model bases on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetic of the enzymatic reaction. The model describes the biosensor response to mixtures of multiple compounds in two regimes of analysis: batch and flow injection. Using computer simulation, large amount of biosensor response data were synthesised for calibration of a biosensor array to be used for characterization of wastewater. The computer simulation was carried out using the finite difference technique.

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