We are concerned here with a three-dimensional nonlinear mixed Volterra-Fredholm integral equations of the second kind which include many key integral that appear in the theory of nonlinear parabolic boundary value pr...
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We are concerned here with a three-dimensional nonlinear mixed Volterra-Fredholm integral equations of the second kind which include many key integral that appear in the theory of nonlinear parabolic boundary value problems. The existence of a unique solution will be proved. A new numerical method for solving these type of equations will be presented. The method is based upon three-dimensional block-pulse functions approximation. In addition convergence analysis of the method is discussed. Illustrative examples are included to demonstrate the validity and applicability of the technique. (C) 2014 Elsevier Inc. All rights reserved.
This paper proposes a new numerical approach for finding the solution of linear time-delay control systems with a quadratic performance index using new hybrid functions. This method is based on a hybrid of block-pulse...
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This paper proposes a new numerical approach for finding the solution of linear time-delay control systems with a quadratic performance index using new hybrid functions. This method is based on a hybrid of block-pulse functions and biorthogonal multiwavelets that consist of cubic Hermite splines on the primal side. The excellent properties of the hybrid functions together with the operational matrices of integration, product, and delay are presented. Using these matrices, the solution of the optimal control of delay systems is reduced to the solution of algebraic equations. Because of the sparsity nature of these matrices, this method is computationally very attractive and reduces CPU time and computer memory. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The effectiveness of the method and the accuracy of the solution are shown in comparison with some other methods by illustrative examples
The operational matrix for performing integration of block-pulse functions is extended to inverse multidimensional Laplace transforms. The inversion algorithm only consists of two simple algebraic operations: multidim...
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The operational matrix for performing integration of block-pulse functions is extended to inverse multidimensional Laplace transforms. The inversion algorithm only consists of two simple algebraic operations: multidimensional bilinear transformation and long division of multivariable polynomials. The method is very suitable for computer programming.
This paper endeavors to formulate block-pulse functions to propose solutions for the Fredholm integral equations system. To begin with we describe the characteristic of block-pulse functions and will go on to indicate...
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This paper endeavors to formulate block-pulse functions to propose solutions for the Fredholm integral equations system. To begin with we describe the characteristic of block-pulse functions and will go on to indicate that through this method a system of Fredholm integral equations can be reduced to an algebraic equation. Numerical examples presented to illustrate the accuracy of the method. (c) 2004 Elsevier Inc. All rights reserved.
This article proposes a simple efficient direct method for solving Volterra integral equation of the first kind. By using block-pulse functions and their operational matrix of integration, first kind integral equation...
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This article proposes a simple efficient direct method for solving Volterra integral equation of the first kind. By using block-pulse functions and their operational matrix of integration, first kind integral equation can be reduced to a linear lower triangular system which can be directly solved by forward substitution. Some examples are presented to illustrate efficiency and accuracy of the proposed method. (C) 2007 Elsevier B.V. All rights reserved.
In this paper, an efficient and effective procedure is successfully developed for parameter identification of linear time-invariant multi-delay systems. The proposed framework is based on a hybrid of block-pulse funct...
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In this paper, an efficient and effective procedure is successfully developed for parameter identification of linear time-invariant multi-delay systems. The proposed framework is based on a hybrid of block-pulse functions and Taylor's polynomials. Two upper error bounds corresponding to hybrid functions are established. The excellent properties of these functions together with the associated operational matrices of integration and delay are utilised to transform the original problem into a system of linear algebraic equations. The least squares method is then implemented for estimation of the unknown parameters. Several numerical experiments are investigated to demonstrate the usefulness and effectiveness of the proposed procedure. Easy implementation, simple operations and accurate solutions are the main features of the suggested approximation scheme.
In this paper, the numerical technique based on hybrid Legendre-block-pulse function has been developed to approximate the solution of system of nonlinear Fredholm-Hammerstein integral equations. These functions are f...
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In this paper, the numerical technique based on hybrid Legendre-block-pulse function has been developed to approximate the solution of system of nonlinear Fredholm-Hammerstein integral equations. These functions are formed by the hybridization of Legendre polynomials and block-pulse functions. These functions are orthonormal and have compact support on [0,1]. The proposed method reduces the system of integral equations to a system of nonlinear algebraic equations that can be solved easily by any usual numerical method. The numerical results obtained by the presented method have been compared with those obtained by Legendre wavelet method (LWM). Numerical examples are presented to illustrate the accuracy of the method. (C) 2015 Elsevier Inc. All rights reserved.
A simple direct method for solving three-dimensional linear Volterra integral equation of the second kind was introduced in this paper. Our method was demonstrated by applying three-dimensional block-pulse functions (...
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A simple direct method for solving three-dimensional linear Volterra integral equation of the second kind was introduced in this paper. Our method was demonstrated by applying three-dimensional block-pulse functions (3D-BPFs) and their operational matrix of integration. Indeed, we converted an integral equation to a linear system that can be easily solved. The convergence analysis of the method was discussed by convergence of 3D-BPFs and we found a bound for the error. Finally, some numerical examples illustrated that our method is feasible and efficient.
In this paper, we present a numerical method based on an NM-set of general hybrid of block-pulse function and Taylor series (HBT), to solve linear Fredholm fuzzy integral equations of the second kind (FFIE-2). Moreove...
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In this paper, we present a numerical method based on an NM-set of general hybrid of block-pulse function and Taylor series (HBT), to solve linear Fredholm fuzzy integral equations of the second kind (FFIE-2). Moreover, the convergence of the proposed method is given. Numerical results with comparisons are given to confirm the reliability of the proposed method for solving these equations. (C) 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.
The main purpose of this paper is to approximate the solution of the optimal control problem for systems governed by a class of nonlinear Volterra integral equations. In order to do this, we use combination of Bernste...
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The main purpose of this paper is to approximate the solution of the optimal control problem for systems governed by a class of nonlinear Volterra integral equations. In order to do this, we use combination of Bernstein polynomials (BPs) and block-pulse functions (BPFs) on the interval [0, 1) for converting this problem to an optimization problem that can be solved easily by mathematical programming techniques. Also, the convergence of the proposed method is discussed. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is applied to some practical problems. (C) 2016 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
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