Journal ArticleDOI
Numerical solution of integral equations system of the second kind by block-pulse functions
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TLDR
The characteristic of Block–Pulse functions is described and it is indicated that through this method a system of Fredholm integral equations can be reduced to an algebraic equation.About:
This article is published in Applied Mathematics and Computation.The article was published on 2005-07-06. It has received 99 citations till now. The article focuses on the topics: Fredholm integral equation & Fredholm theory.read more
Citations
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A new approach based on semi-orthogonal B-spline wavelets for the numerical solutions of the system of nonlinear Fredholm integral equations of second kind
P. K. Sahu,Soumya Ray +1 more
TL;DR: In this paper, a new approach based on linear B-spline wavelet method has been developed to approximate the solutions of system of nonlinear Fredholm integral equations of second kind.
Journal ArticleDOI
The construction of operational matrix of fractional integration using triangular functions
Khosrow Maleknejad,M. Asgari +1 more
TL;DR: In this article, the operational matrix of triangular functions for fractional order integration in the Caputo sense is derived and applied for solving multi-order fractional differential equations, Abel's integral equations and nonlinear integro-differential equations.
Numerical solution of system of linear integral equations via improvement of block-pulse functions
TL;DR: In this article, a numerical method based on block-pulse functions (IBPFs) is discussed for solving the system of linear Volterra and Fredholm integral equations, which can be reduced to a linear system of algebraic equations.
Journal ArticleDOI
Numerical solution of fractional Mathieu equations by using block-pulse wavelets
TL;DR: In this paper, a block-pulse wavelets matrix of fractional order integration with respect to the Caputo sense is used for numerical solution of fraction fractional Mathieu equation and then applied in a number of cases.
Hybrid Orthonormal Bernstein and Block-Pulse Functions for Solving Fredholm Integral Equations
TL;DR: In this article, a combination of orthonormal Bernstein and block-pulse functions was used to solve the linear Fredholm integral equations of the second kind, and the result of the proposed method was compared with true answers to show the convergence and advantages of the new method.
References
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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.
Book
Piecewise Constant Orthogonal Functions and Their Application to Systems and Control
TL;DR: In this article, the authors proposed piecewise constant orthogonal basis functions (PCF) for linear and non-linear linear systems, and the optimal control of linear lag-free and time-lag systems.
Journal ArticleDOI
Analysis and synthesis of dynamic systems via block-pulse functions
TL;DR: The paper presents a method of numerically integrating a system of differential equations based on an idea of orthogonal approximation of functions that gives piecewise constant solutions with minimal mean-square error and is computationally similar to the familiar trapezoidal rule of integration.
Journal ArticleDOI
Design of piecewise constant gains for optimal control via Walsh functions
Chih-Fan Chen,Chi-Huang Hsiao +1 more
TL;DR: This paper presents a technique for determinating time-varying feedback gains of linear systems with quadratic performance criteria by developing an operational matrix for solving state equations and solving the piecewise constant gains problem.