Journal ArticleDOI
A new set of orthogonal functions and its application to the analysis of dynamic systems
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It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.Abstract:
The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.read more
Citations
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Analysis of time delay systems via new triangular functions
TL;DR: In this paper, the authors presented a numerical method for finding the solution of time-delay systems using triangular functions, where the operational matrices of integration and delay are utilized to reduce the solution to the solution for algebraic equations.
Journal ArticleDOI
Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations
Mahnaz Asgari,Morteza Khodabin +1 more
TL;DR: In this article, a new numerical method based on triangular functions for solving nonlinear stochastic differential equations is presented, which is very simple and attractive, and convergence analysis and numerical examples that illustrate accuracy and efficiency of the method are presented.
Journal ArticleDOI
A New Approach based on Triangular Functions for Solving N-dimensional Stochastic Differential Equations
TL;DR: In this paper, a new numerical method based on triangular functions for solving n-dimensional stochastic differential equations is presented, and convergence analysis and numerical examples illustrate accuracy and efficiency of this approach.
Journal ArticleDOI
Operational matrix method for solving fractional weakly singular 2D partial Volterra integral equations
Isa Zamanpour,Reza Ezzati +1 more
TL;DR: In this paper , the authors proposed an expansion of the operational matrix for fractional integration of triangular functions to find the numerical solution of non-linear fractional weakly singular two-dimensional partial Volterra integral equations.
Preconditioned Technique for Solving Fredholm Integral Equations of the First Kind with Orthogonal Triangular Functions
TL;DR: In this article, a numerical approach based on an m-set of general, orthogonal triangular functions (TF) is proposed to approximate the solution of Fredholm integral equations of the first kind.
References
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Zur Theorie der orthogonalen Funktionensysteme
TL;DR: In der Theorie der Reihenentwicklung der reellen Funktionen spielen die sog. orthogonalen Funktionensysteme eine fuhrende Rolle.
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Identification of continuous-time systems
G.P. Rao,Heinz Unbehauen +1 more
TL;DR: Continuous-time model-based system identification as mentioned in this paper is a well-established field in the field of control systems and is concerned with the determination of particular models for systems that are intended for a certain purpose such as control.
Journal ArticleDOI
Walsh operational matrices for fractional calculus and their application to distributed systems
C.F. Cheng,Y.T. Tsay,Tao Wu +2 more
TL;DR: In this paper, the Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems and a new set of orthogonal functions is derived from Walsh functions.