جستجوی مقالات مرتبط با کلیدواژه « Modification of Hat functions » در نشریات گروه « ریاضی »

A system of integral equations can describe different kind of problems in sciences and engineering. There are many different methods for numerical solution of linear and nonlinear system of integral equations.
This paper proposed a numerical method based on modification of Hat functions for solving system of Fredholm-Hammerstein integral equations. The proposed method reduced a system of integral equation to a system of algebraic equations that can be solved easily by known methods.
For showing the accuracy and capability of the proposed method, some numerical examples are proposed that their results compared by results of other methods, and shows the capability and the superiority of this method to other existed methods.
Also this paper derived the computational cost and the error analysis of the proposed method.
The following conclusions were drawn from this research.


This paper proposed a numerical method based on modification of Hat functions for solving system of Fredholm-Hammerstein integral equations.
The proposed method reduced a system of integral equation to a system of algebraic equations that can be solved easily by known methods.
The presented error analysis and solved problems show capability and the superiority of this method to other existed methods../files/site1/files/52/1.pdf

In this paper, we consider the numerical solution of a class of delay fractional optimal control problems using modification of hat functions. First, we introduce the fractional calculus and modification of hat functions. Fractional integral is considered in the sense of Riemann-Liouville and fractional derivative is considered in the sense of Caputo. Then, operational matrix of fractional integration, product and delay operational matrix of the basis functions vector are introduced. For solving the optimal control problem, all functions in the problem are approximated using the basis functions. A system of nonlinear algebraic equations are obtained using the properties of modification of hat functions and the introduced operational matrices. By solving the obtained system, the unknown coefficients of the state and control input functions are determined and by substituting these values an approximation of the solution of the problem is given. Finally, some examples of different kinds of delay fractional optimal control problems are considered to confirm the accuracy and applicability of the suggested method.

In this article, we have discussed a new application of modification of hat functions on nonlinear multi-order fractional differential equations. The operational matrix of fractional integration is derived and used to transform the main equation to a system of algebraic equations. The method provides the solution in the form of a rapidly convergent series. Furthermore, error analysis of the proposed method is provided under several mild conditions. Three numerical examples are given to show the efficiency and accuracy of the method. Illustrative examples are included to demonstrate the validity, efficiency, and applicability of the method.