This study aims to present a computational method for solving Abel's integral equation of the second kind. The introduced method is based on the use of block-pulse functions (BPFs) via collocation method. Abel'...
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This study aims to present a computational method for solving Abel's integral equation of the second kind. The introduced method is based on the use of block-pulse functions (BPFs) via collocation method. Abel's integral equations as singular Volterra integral equations are hard and heavy in computation, but because of the properties of BPFs, as is reported in examples, this method is more efficient and more accurate than some other methods for solving this class of integral equations. On the other hand, the benefit of this method is low cost of computing operations. The applied method transforms the singular integral equation into triangular linear algebraic system that can be solved easily. An error analysis is worked out and applications are demonstrated through illustrative examples.
We construct two-dimensional hybrid functions from Lagrange polynomials and block-pulse functions. Using special properties of the functions for evaluating integral and derivatives, we develop an efficient algorithm f...
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In this paper, first, a numerical method is presented for solving generalized linear and nonlinear second-order two point initial and boundary value problems. The operational matrix of derivative is obtained by introd...
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In this paper, first, a numerical method is presented for solving generalized linear and nonlinear second-order two point initial and boundary value problems. The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and block-pulse functions. The obtained operational matrix is used to reduce the linear or nonlinear equations with their initial or boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. Finally, the efficiency of the proposed method is indicated by some numerical examples.
This paper deals with the solutions of linear fuzzy Fredholm integral equation systems by using a combination of Bernstein and block-pulse functions on the interval [0, 1), that is called hybrid functions. Moreover, t...
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This paper deals with the solutions of linear fuzzy Fredholm integral equation systems by using a combination of Bernstein and block-pulse functions on the interval [0, 1), that is called hybrid functions. Moreover, the existence of the solution and convergence of the proposed method is proved. Finally, illustrative examples are included in order to demonstrate the accuracy and the convergence of this method. (C) 2014 Taibah University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/3.0/).
In this article a robust approach for solving mixed nonlinear Volterra-Fredholm type integral equations of the first kind is investigated. By using the modified two-dimensional block-pulse functions (M2D-BFs) and thei...
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Using the operational properties of general block-pulse functions and Chebyshev polynomials, the neutral functional differential systems are transformed into a system of algebraic equations. The numerical solutions of...
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Using the operational properties of general block-pulse functions and Chebyshev polynomials, the neutral functional differential systems are transformed into a system of algebraic equations. The numerical solutions of the systems are derived. Moreover, applying the results to the linear quadratic optimal control problems, the approximate solutions of optimal control for the neutral functional differential systems are obtained.
Reference is made to paper 2679D left bracket IEE Proc. D, Control Theory & Appl. , 1983, 130, (5), pp. 250-254 right bracket by C. Hwang, T. -Y. Guo and Y. -P. Shih. It is claimed that certain citations from the ...
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Reference is made to paper 2679D left bracket IEE Proc. D, Control Theory & Appl. , 1983, 130, (5), pp. 250-254 right bracket by C. Hwang, T. -Y. Guo and Y. -P. Shih. It is claimed that certain citations from the literature were left out. A response by the original authors is included.
This is an erratum to the published paper “Numerical solution of linear Fredholm integral equation by using hybrid Taylor and block-pulse functions” by Maleknejad and Mahmoudi, where there are some scientific errors...
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This is an erratum to the published paper “Numerical solution of linear Fredholm integral equation by using hybrid Taylor and block-pulse functions” by Maleknejad and Mahmoudi, where there are some scientific errors. After considering these errors we attempt to rectify them by presenting correct approach and formulae. Moreover, by means of some numerical examples, we illustrate the accuracy of solutions after applying the correct formulae.
A method for identifying a class of non-linear distributed systems is presented by using two dimension block-pulse functions. An error analysis for the approximation is emphasized and made first. The optimal selection...
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A method for identifying a class of non-linear distributed systems is presented by using two dimension block-pulse functions. An error analysis for the approximation is emphasized and made first. The optimal selection of the numbers of the truncated terms is discussed by using non-liner integer programming. Appropriate examples are included to illustrate the ideas.
The quasilinearization technique used for state and parameter identification to nonlinear system is studied via block-pulse functions. Making use of the integral properties of block-pulse functions, an algorithm is pr...
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The quasilinearization technique used for state and parameter identification to nonlinear system is studied via block-pulse functions. Making use of the integral properties of block-pulse functions, an algorithm is presented which reduces the well known quasilinearization technique to that of solving a set of algebraic equations. These results appear to simplify the numerical effort involved in solving state and parameter estimation problems.
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