In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

in this paper, an efficient method for solving optimal control problemsof the linear differential systems with inequality constraint is proposed. by usingnew adjustment of hat basis functions and their operational matrices of integration,optimal control problem is reduced to an optimization problem. also, the erroranalysis of the proposed method is investigated and it is proved that the order o...

alternative legendre polynomials (alps) are used to approximate the solution of a class of nonlinear volterra-hammerstein integral equations. for this purpose, the operational matrices of integration and the product for alps are derived. then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. the error analysis of the method is given an...

In this study, the Bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. To this aim, the operational matrices of integration and the product for Bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. Some examples are presented to illustrate the efficien...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by...

In this paper, an efficient method for solving optimal control problems of the linear differential systems with inequality constraint is proposed. By using new adjustment of hat basis functions and their operational matrices of integration, optimal control problem is reduced to an optimization problem. Also, the error analysis of the proposed method is nvestigated and it is proved that the orde...

In this paper, the wavelet method based on the Chebyshev polynomials of the second kind is introduced and used to solve systems of integral equations. Operational matrices of integration, product, and derivative are obtained for the second kind Chebyshev wavelets which will be used to convert the system of integral equations into a system of algebraic equations. Also, the error is analyzed and ...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...