A Unifying Method to Construct Rational Basis Functions for Linear and Nonlinear Systems

2017 ◽  
Vol 37 (6) ◽  
pp. 2394-2412
Author(s):  
Ricardo Schumacher ◽  
Gustavo H. C. Oliveira
Keyword(s):  
Nonlinear Systems ◽  
Basis Functions ◽  
Rational Basis ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

scholarly journals Bezier Polynomials with Applications

2018 ◽  
Vol 66 (2) ◽  
pp. 157-162
Author(s):  
Nazrul Islam ◽  
Md Shafiqul Islam
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Boundary ◽  
Approximate Solutions ◽  
Basis Functions ◽  
Tabular Form ◽  
Nonlinear Boundary Value Problems ◽  
Matrix Formulation ◽  
Linear And Nonlinear ◽  
The Galerkin Method ◽  
Linear And Nonlinear Systems

In this paper, we use the Galerkin technique for solving higher order linear and nonlinear boundary value problems (BVPs). The well-known Bezier polynomials are exploited as basis functions in the technique. To use the Bezier polynomials, we need to satisfy the corresponding homogeneous form of the boundary conditions and modification is thus needed. A rigorous matrix formulation is developed by the Galerkin method for linear and nonlinear systems and solved it using Bezier polynomials. The approximate solutions are compared to the exact solutions through tabular form. All problems are computed using the software MATHEMATICA. Dhaka Univ. J. Sci. 66(2): 157-162, 2018 (July)

Mathematical modeling of conversion of non-Gaussian random processes, signals and noise in linear and nonlinear systems

2018 ◽  
pp. 66-78
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Systems ◽  
Random Processes ◽  
Mathematical Transformation ◽  
Positive And Negative Feedback ◽  
Non Linear Systems ◽  
Linear And Nonlinear ◽  
Non Gaussian ◽  
Linear And Nonlinear Systems ◽  
Inertial Systems

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

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