Triangular Orthogonal Functions for the Analysis of Continuous Time Systems

Deb, Argha; Sarkar, Gautam; Sengupta, Anindita

doi:10.7135/upo9781843318118

Cited by 35 publications

(28 citation statements)

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“…Multiplication of triangular functions and related properties were first treated in [26]. It can be concluded from orthogonality of TFs that…”

Section: Multiplication Of Tfsmentioning

confidence: 99%

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An efficient hybrid method for solving fredholm integral equations using triangular functions

Ali¹,

Ramadan²

2017

ntmsci

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Abstract:In this paper the orthogonal triangular function (TF) based method is first applied to transform the Fredholm integral equations and Fredholm system of integral equations to a coupled system of matrix algebraic equations. The obtained system is a variant of coupled Sylvester matrix equations. A finite iterative algorithm is then applied to solve this system to obtain the coefficients used to get the form of approximate solution of the unknown functions of the integral problems. Some numerical examples are solved to illustrate the accuracy and the efficiency of the proposed hybrid method. The obtained numerical results are compared with other numerical methods and the exact solutions.

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“…Multiplication of triangular functions and related properties were first treated in [26]. It can be concluded from orthogonality of TFs that…”

Section: Multiplication Of Tfsmentioning

confidence: 99%

“…We concerned with iterative solutions to coupled system of like forms of the Sylvester matrix equations [26]. There are many variant forms of finite iterative algorithms for solving matrix equation.…”

Section: Triangular Functions (Tfs) For Function Approximationmentioning

confidence: 99%

An efficient hybrid method for solving fredholm integral equations using triangular functions

Ali¹,

Ramadan²

2017

ntmsci

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“…In this paper for convergence of the proposed method, we supposed that m 1 = m 2 = m 3 = m 4 = m. More details about the properties of the triangular functions are given in [5,8].…”

Section: Approximate the Function With 2d-tfsmentioning

confidence: 99%

“…The set of triangular orthogonal functions (TFs) has been presented and applied to analysis of dynamical systems. These functions was first treated by Deb et al [5,6]. Recently, introduced triangular orthogonal functions have been applied for solving Volterra Fredholm integral equation and integral equation system by Babolian et al [2,4] and Almasieh et al [1].…”

Section: Introductionmentioning

confidence: 99%

Solving linear two-dimensional Fredholm integral equations system by triangular functions

Asl

Nadjafi

2016

IJAMR

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In this paper, we intend to offer a numerical method to solve linear two-dimensional Fredholm integral equations system of the second kind. This method converts the given two-dimensional Fredholm integral equations system into a linear system of algebraic equations by using two-dimensional triangular functions. Moreover, we prove the convergence of the method. Finally the proposed method is illustrated by two examples and also results are compared with the exact solution by using computer simulations.

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“…Marriage of sample-and-hold functions (SHF) [1] and triangular functions (TF) [1] has given birth to a set of orthogonal hybrid functions (HF) [2][3]. Among various utilities and applications of HF, this paper is focused on System Analysis.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Function Based Analysis of Simple Networks

Sarkar¹,

Purkait

Ganguly

et al. 2014

Advanced Computing, Networking and Informatics- Volume 2

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Abstract. This paper represents a method of analysis of simple networks with the help of MATLAB-SIMULINK models and microcontroller based hardware. The mathematical foundation of this method is an algorithm based on orthogonal Hybrid Function.Keywords: Hybrid function, microcontroller, MATLAB, analysis. IntroductionMarriage of sample-and-hold functions (SHF) [1] and triangular functions (TF) [1] has given birth to a set of orthogonal hybrid functions (HF) [2][3]. Among various utilities and applications of HF, this paper is focused on System Analysis. Hybrid Function -A Combination of Shf and TfWe can use a set of sample-and-hold functions and the set of triangular functions to form a function set, which we call a 'Hybrid Function' set. To define this set, we express the (i+1)-th member H i (t)of the m-set hybrid function H m (t)where, i = 0, 1, 2, …, (m-1), a i and b i are scaling constants. We can approximate a square integrable function f(t) of Lebesgue measure by Hybrid Function set. Fig. 1 illustrates this idea. f(t) is sampled at three equidistant points A,C,E. c 0 , c 1 , c 2 are the magnitude of these samples. Linearly joining A, C& C,E we get a SHF set composed of □ABFO &□CDGF and TF set constituted with ∆ACB & ∆CED. Hence, piecewise linear wave which we get in this manner, is nothing but HFapproximation of f(t).

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Triangular Orthogonal Functions for the Analysis of Continuous Time Systems

Abstract: This book deals with a new set of triangular orthogonal functions, which evolved from the set of well known block pulse functions (BPF), a major member of the piecewise constant orthogonal function (PCOF) family.

Cited by 35 publications

References 0 publications

An efficient hybrid method for solving fredholm integral equations using triangular functions

An efficient hybrid method for solving fredholm integral equations using triangular functions

Solving linear two-dimensional Fredholm integral equations system by triangular functions

Hybrid Function Based Analysis of Simple Networks

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