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Numerical solution of nonlinear two-dimensional integral equations using rationalized haar functions

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2011年第3期16卷 1164-1175页

作者： Babolian, E. Bazm, S. Lima, P. Tarbiat Moallem Univ Fac Math Sci & Comp Tehran *** Iran Univ Tecn Lisboa Inst Super Tecn CEMAT P-1049001 Lisbon Portugal Univ Tecn Lisboa Inst Super Tecn Dept Matemat P-1049001 Lisbon Portugal

Two-dimensional rationalized haar (RH) functions are applied to the numerical solution of nonlinear second kind two-dimensional integral equations. Using bivariate collocation method and Newton Cotes nodes, the numerical solution of these equations is reduced to solving a nonlinear system of algebraic equations. Also, some numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Two-dimensional integral equations Nonlinear integral equations rationalized haar functions Bivariate collocation method

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Solving optimal control problems of the time-delayed systems by haar wavelet

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JOURNAL OF VIBRATION AND CONTROL 2016年第11期22卷 2657-2670页

作者： Nazemi, Alireza Mansoori, Masoomeh Shahrood Univ Dept Math POB ***-316 Shahrood Iran

We consider an approximation scheme using haar wavelets for solving time-delayed optimal control problems with terminal inequality constraints. The problem is first transformed, using a Pade approximation, to one without a time-delayed argument. Terminal inequality constraints, if they exist, are converted to equality constraints via Valentine-type unknown parameters. A computational method based on haar wavelets in the time domain is then proposed for solving the obtained nondelay optimal control problem. The haar wavelets integral operational matrix and direct collocation method are utilized to find the approximated optimal trajectory and the optimal control law of the original problem. Numerical results are also given for several test examples to demonstrate the applicability and the efficiency of the method.

关键词： Time-delayed optimal control problems approximation terminal condition rationalized haar functions nonlinear programming

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Solving fractional optimal control problems with fixed or free final states by haar wavelet collocation method

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2016年第2期33卷 543-561页

作者： Hosseinpour, Soleiman Nazemi, Alireza Univ Shahrood Sch Math Sci Dept Math POB ***-316 Shahrood Iran

A numerical method using haar wavelets for solving fractional optimal control problems (FOCPs) is studied. The fractional derivative in these problems is in the Caputo sense. The operational matrix of fractional Riemann-Liouville integration and the direct collocation method are considered. The proposed technique is applied to transform the state and control variables into non-linear programming (NLP) parameters at collocation points. An NLP solver can then be used to solve FOCPs. Illustrative examples are included to demonstrate the validity and applicability of the proposed method.

关键词： fractional optimal control problems Caputo derivative rationalized haar functions operational matrix non-linear programming

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Solving infinite-horizon optimal control problems of the time-delayed systems by haar wavelet collocation method

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COMPUTATIONAL & APPLIED MATHEMATICS 2016年第1期35卷 97-117页

作者： Mansoori, Masoomeh Nazemi, Alireza Shahrood Univ Sch Math Sci Dept Math POB ***-316 Shahrood Iran

A numerical method using haar wavelets for solving infinite-horizon time-delayed optimal control problems is studied. The problem is first transformed, using a Pade approximation, to one without a time-delayed argument. By a suitable change of variable, the obtained non-delay infinite-horizon optimal control problem is converted to a finite-horizon non-linear optimal control problem. An approximation scheme based on haar wavelets in the time domain is then proposed for solving the obtained optimal control problem. haar wavelets integral operational matrix and direct collocation method are used to find the approximated optimal trajectory and the optimal control law of the original problem. Two illustrative examples are provided to show the feasibility and the efficiency of the proposed method.

关键词： Infinite-horizon Time-delayed Optimal control problems Approximation rationalized haar functions Non-linear programming

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AWAVELET COLLOCATION SCHEME FOR SOLVING SOME OPTIMAL PATH PLANNING PROBLEMS

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ANZIAM JOURNAL 2016年第4期57卷 461-481页

作者： Mortezaee, Marziyeh Nazemi, Alireza Shahrood Univ Technol Sch Math Sci Dept Math POB ***-316 Shahrood Iran

We consider an approximation scheme using haar wavelets for solving optimal path planning problems. The problem is first expressed as an optimal control problem. A computational method based on haar wavelets in the time domain is then proposed for solving the obtained optimal control problem. A haar wavelets integral operational matrix and a direct collocation method are used to find an approximate optimal trajectory of the original problem. Numerical results are also presented for several examples to demonstrate the applicability and efficiency of the proposed method.

关键词： optimal path planning problems approximation rationalized haar functions nonlinear programming

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Numerical computational solution of the linear Volterra integral equations system via rationalized haar functions

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Journal of King Saud University - Science 2010年第4期22卷 265-268页

作者： Mirzaee, Farshid Department of Mathematics Faculty of Science Malayer University Malayer 65719-95863 Iran

In this paper, we use rationalized haar (RH) functions to solve the linear Volterra integral equations system. We convert the integral equations system, to a system of linear equations. We show that our estimates have... 详细信息

关键词： Operational matrix Product operation rationalized haar functions Volterra integral equations system

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Numerical solution of linear time-varying differential equations using the hybrid of block-pulse and rationalized haar functions

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JOURNAL OF VIBRATION AND CONTROL 2006年第10期12卷 1081-1092页

作者： Arabzadeh, B. Razzaghi, M. Ordokhani, Y. Amirkabir Univ Technol Dept Appl Math Tehran Iran Mississippi State Univ Dept Math & Stat Mississippi State MS 39762 USA Alzahra Univ Dept Math Tehran Iran

A numerical method for finding the solution of linear time-varying differential equations is proposed. The properties of the hybrid functions, which consist of block-pulse functions plus rationalized haar functions, are presented. The properties of the hybrid functions together with the operational matrices of integration and product are then utilized to reduce the solution of differential equations to the solution of algebraic equations. Examples are included to demonstrate the validity and applicability of the technique.

关键词： hybrid rationalized haar functions block-pulse functions differential equations

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rationalized haar approach for nonlinear constrained optimal control problems

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APPLIED MATHEMATICAL MODELLING 2010年第1期34卷 174-183页

作者： Marzban, H. R. Razzaghi, M. Mississippi State Univ Dept Math & Stat Mississippi State MS 39762 USA Isfahan Univ Technol Dept Math Esfahan Iran Amirkabir Univ Dept Appl Math Tehran Iran

This paper presents a numerical method for solving nonlinear optimal control problems including state and control inequality constraints. The method is based upon rationalized haar functions. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique. (C) 2009 Elsevier Inc. All rights reserved.

关键词： rationalized haar functions Optimal control Nonlinear Inequality constraint

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Solving linear integro-differential equations system by using rationalized haar functions method

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APPLIED MATHEMATICS AND COMPUTATION 2004年第2期155卷 317-328页

作者： Maleknejad, K Mirzaee, F Abbasbandy, S Iran Univ Sci & Technol Sch Math Tehran 16844 Iran Imam Khomeini Int Univ Qazvin 34194 Iran

In this paper, we use rationalized haar functions to estimate the solution of linear integro-differential equations system. Properties of rationalized haar functions are first presented, and the operational matrix of the product of two rationalized haar functions vector is utilized to reduce the computation of linear integro-differential equations system to some algebraic equations. By using numerical examples we show our estimation have a good degree of accuracy. (C) 2003 Elsevier Inc. All rights reserved.

关键词： linear integro-differential equations system operational matrix product operation rationalized haar functions

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Numerical solution of linear Fredholm integral equations system by rationalized haar functions method

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2003年第11期80卷 1397-1405页

作者： Maleknejad, K Mirzaee, F Iran Univ Sci & Technol Sch Math Tehran 16844 Iran

In this paper rationalized haar functions are developed to approximate the solutions of the linear Fredholm integral equations system. Properties of rationalized haar functions are first presented, the operational matrix of the product of rationalized haar functions vector is utilized to reduce the computation of Fredholm integral equations system to some algebraic equations. Finally, numerical result are given which support the theoretical results.

关键词： linear Fredholm integral equations system operational matrix product operation rationalized haar functions

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