General response formula for two-dimensional linear systems with variable coefficients

1986 ◽  
Vol 31 (3) ◽  
pp. 278-280 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Variable Coefficients ◽  
Two Dimensional ◽  
General Response ◽  
Response Formula

OPTIMAL CONTROL FOR TWO-DIMENSIONAL LINEAR SYSTEMS WITH VARIABLE COEFFICIENTS

2008 ◽  
Vol 1 (4) ◽  
pp. 245-257 ◽  
Author(s):  
Jimshone Li ◽  
Jason Sheng-Hong Tsai ◽  
Leang-San Shieh
Keyword(s):  
Optimal Control ◽  
Linear Systems ◽  
Variable Coefficients ◽  
Two Dimensional

Two-Dimensional Legendre Wavelets for Solving Variable-Order Fractional Nonlinear Advection-Diffusion Equation with Variable Coefficients

2018 ◽  
Vol 19 (7-8) ◽  
pp. 793-802 ◽  
Author(s):  
M. Hosseininia ◽  
M. H. Heydari ◽  
Z. Avazzadeh ◽  
F. M. Maalek Ghaini
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Main Idea ◽  
Variable Coefficients ◽  
Variable Order ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Nonlinear Advection

AbstractThis article studies a numerical scheme for solving two-dimensional variable-order time fractional nonlinear advection-diffusion equation with variable coefficients, where the variable-order fractional derivative is in the Caputo type. The main idea is expanding the solution in terms of the 2D Legendre wavelets (2D LWs) where the variable-order time fractional derivative is discretized. We describe the method using the matrix operators and then implement it for solving various types of fractional advection-diffusion equations. The experimental results show the computational efficiency of the new approach.

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