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 ...

A modification of the homotopy analysis method (HAM) for solving a system of nonlinear boundary value problems (BVPs) in semi–infinite domain, micropolar flow due to a linearly stretching of porous sheet, is proposed. This method is based on operational matrix of exponential Chebyshev functions to construct the derivative and product of the unknown function in the matrix form. In addition, by u...

in this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. the sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. then, the newton-raphson method is used for solving these sets of algebraic equations. to present ability ...

In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. We derived the operational matrix of fractional integration of cubic and pantic B-spline scaling functions and used them to transform the mentioned equations to a syste...

In this paper, we extend the operational matrix method to solve tempered fractional differential equation, via shifted Legendre polynomial. Although is widely used in solving various calculus problems, it yet apply equations defined derivatives. We first derive analytical expression for derivative x p</...

in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

the current paper proposes a technique for the numerical solution of linear control systems.the method is based on galerkin method, which uses the interpolating scaling functions. fora highly accurate connection between functions and their derivatives, an operational matrix forthe derivatives is established to reduce the problem to a set of algebraic equations. several testproblems are given, a...

fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. therefore, a reliable and efficient technique as a solution is regarded.this paper develops approximate solutions for boundary value problems ofdifferential equations with non-integer order by using the shannon waveletbases. wavelet bases have d...

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...