Hybrid Of Block-pulse Functions Research Articles

Optimal Control of Time Delay Systems via Hybrid of Block-Pulse Functions and Orthonormal Taylor Series

A new method to find the optimal control of time delay systems with quadratic performance index is discussed. The method is based on hybrid functions. The properties of the hybrid functions which consists of block-pulse functions and orthonormal Taylor series are presented. The operational matrices of integration, delay, dual and product are used to reduce the solution of optimal control time delay system to the solution of algebraic equations. Numerical examples are included to illustrate the effectiveness and validity of the technique.

Numerical solution of nonlinear fuzzy Fredholm integral equations of the second kind using hybrid of block-pulse functions and Taylor series

The main purpose of this paper is to introduce a method of successive approximations in terms of a hybrid of Taylor series and a block-pulse function, which is given for solving nonlinear fuzzy Fredholm integral equations of the second kind and the error estimate of the approximation solution. Finally, two numerical examples are presented to show the accuracy of the proposed method.

Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models 2014

Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models 2014

Retracted: Numerical Solution of Nonlinear Fredholm Integrodifferential Equations by Hybrid of Block-Pulse Functions and Normalized Bernstein Polynomials

Retracted: Numerical Solution of Nonlinear Fredholm Integrodifferential Equations by Hybrid of Block-Pulse Functions and Normalized Bernstein Polynomials

A hybrid approximation scheme for discretizing constrained quadratic optimal control problems

In this paper, a composite Chebyshev finite difference method for solving linear quadratic optimal control problems with inequality constraints on state and control variables is introduced. This method is an extension of Chebyshev finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well known Chebyshev–Gauss–Lobatto nodes. The excellent properties of hybrid functions are used to convert optimal control problem into a mathematical programming problem whose solution is much more easier than the original one. Various types of optimal control problems are investigated to demonstrate the effectiveness of the proposed approximation scheme. The method is simple, easy to implement and provides very accurate results.

Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

A computational method based on hybrid of block-pulse functions and Taylor series for solving two-dimensional nonlinear integral equations

In this paper, a new reliable technique, which is based on hybrid functions approximation, is introduced for the approximate solutions of two-dimensional nonlinear Fredholm and Volterra integral equations. The properties of block-pulse functions together with the Taylor series are used to reduce the problem to the solution of nonlinear algebraic equations. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results show reliability and efficiency of the proposed method.

RETRACTED: Solution of nonlinear Fredholm integro-differential equations using a hybrid of block pulse functions and normalized Bernstein polynomials

A numerical method for solving nonlinear Fredholm integro-differential equations is proposed. The method is based on hybrid function approximations. The properties of a hybrid of block pulse functions and orthonormal Bernstein polynomials are presented and utilized to reduce the problem to the solution of nonlinear algebraic equations. Numerical examples are introduced to illustrate the effectiveness and simplicity of the present method.

Numerical Method in Solving Fredholm Integro-differential Equations by Using Hybrid Function Operational Matrix of Derivative

A numerical method for solving Fredholm integro-differential equations is introduced. The method is based upon hybrid functions and tau method. A hybrid function operational matrix of derivative is presented. The properties of hybrid of block-pulse functions and Chebyshev polynomials are utilized to reduce the integro-differential equations to the solution of algebraic equations. The efficiency of and accuracy of the proposed method is illustrated by three examples.

Numerical solution of nonlinear Volterra–Fredholm integral equations using hybrid of block-pulse functions and Taylor series

A numerical method based on an NM-set of general, hybrid of block-pulse function and Taylor series (HBT), is proposed to approximate the solution of nonlinear Volterra–Fredholm integral equations. The properties of HBT are first presented. Also, the operational matrix of integration together with Newton-Cotes nodes are utilized to reduce the computation of nonlinear Volterra–Fredholm integral equations into some algebraic equations. In addition, convergence analysis and numerical examples that illustrate the pertinent features of the method are presented.

Numerical Solution of Nonlinear Fredholm Integrodifferential Equations by Hybrid of Block-Pulse Functions and Normalized Bernstein Polynomials

A numerical method for solving nonlinear Fredholm integrodifferential equations is proposed. The method is based on hybrid functions approximate. The properties of hybrid of block pulse functions and orthonormal Bernstein polynomials are presented and utilized to reduce the problem to the solution of nonlinear algebraic equations. Numerical examples are introduced to illustrate the effectiveness and simplicity of the present method.

On Solution of Fredholm Integrodifferential Equations Using Composite Chebyshev Finite Difference Method

A new numerical method is introduced for solving linear Fredholm integrodifferential equations which is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well-known Chebyshev-Gauss-Lobatto collocation points. Composite Chebyshev finite difference method is indeed an extension of the Chebyshev finite difference method and can be considered as a nonuniform finite difference scheme. The main advantage of the proposed method is reducing the given problem to a set of algebraic equations. Some examples are given to approve the efficiency and the accuracy of the proposed method.

A composite Chebyshev finite difference method for nonlinear optimal control problems

In this paper, a composite Chebyshev finite difference method is introduced and is successfully employed for solving nonlinear optimal control problems. The proposed method is an extension of the Chebyshev finite difference scheme. This method can be regarded as a non-uniform finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well-known Chebyshev–Gauss–Lobatto points. The convergence of the method is established. The nice properties of hybrid functions are then used to convert the nonlinear optimal control problem into a nonlinear mathematical programming one that can be solved efficiently by a globally convergent algorithm. The validity and applicability of the proposed method are demonstrated through some numerical examples. The method is simple, easy to implement and yields very accurate results.

Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid Functions and the Collocation Method

A numerical method to solve nonlinear Fredholm integral equations of second kind is presented in this work. The method is based upon hybrid function approximate. The properties of hybrid of block‐pulse functions and Taylor series are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of algebraic equations. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Solution of nonlinear delay optimal control problems using a composite pseudospectral collocation method

We develop a composite collocation approximation scheme for thenumerical solution of nonlinear delay optimal control problems.For this purpose, we present an extension and also modificationfor the Gauss pseudospectral method using the hybrid ofblock-pulse functions and Lagrange polynomials based on theLegendre-Gauss points. In this respect, we derive thecorresponding operational matrix of derivative according to theweak representation of derivative operator. In order todemonstrate the applicability, efficiency and accuracy of theproposed method, we examine two illustrative examples.

Solution of variational problems via hybrid of block-pulse and Lagrange interpolating

A direct method for solving variational problems using the hybrid of block-pulse functions and Lagrange interpolating polynomials is presented. The method is based upon hybrid functions approximations. The properties of hybrid functions, which consist of block-pulse functions and Lagrange interpolating polynomials, are presented. These properties are then utilised to reduce the variational problems to the solution of non-linear equations. Three examples are considered, in the first example the classical brachistochrone problem is studied and in the second and third examples, two non-linear problems are examined. The method is general, easy to implement and yields very accurate results.

Numerical solutions of optimal control for time delay systems by hybrid of block-pulse functions and Legendre polynomials

Using the operational properties of general block-pulse functions and Legendre polynomials, the linear inverse time 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 of time delay systems are derived.

Analysis of Time-delay Systems via Hybrid of Block-pulse Functions and Taylor Series

In this paper we present a method for finding the solution of time-delay systems using a hybrid function. We present the properties of the hybrid functions, which consist of block-pulse functions plus Taylor series. The method is based upon expanding various time functions in the system as their truncated hybrid functions. Operational matrices of integration and delay are presented and are utilized to reduce the solution of time-delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Solution of multi-delay systems using hybrid of block-pulse functions and Taylor series

A method for finding the solution of linear time-varying multi-delay systems using a hybrid function is proposed. The properties of the hybrid functions which consist of block-pulse functions plus Taylor series are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. Operational matrices of integration, delay and product are presented and are utilized to reduce the solution of multi-delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.