this paper gives an ecient numerical method for solving the nonlinear systemof volterra-fredholm integral equations. a legendre-spectral method based onthe legendre integration gauss points and lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

In this paper, a numerical efficient method is proposed for the solution of time fractional mobile/immobile equation. The fractional derivative of equation is described in the Caputo sense. The proposed method is based on a finite difference scheme in time and Legendre spectral method in space. In this approach the time fractional derivative of mentioned equation is approximated by a scheme of ord...

‎A numerical technique based on the collocation method using Legendre multiwavelets are‎ ‎presented for the solution of forced Duffing equation‎. ‎The operational matrix of integration for ‎Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation‎ ‎to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate‎ ‎the valid...

This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

In this paper, we develop a framework to obtain approximate numerical solutions to ordi‌nary differential equations (ODEs) involving fractional order derivatives using Legendre wavelets approximations. The continues Legendre wavelets constructed on [0, 1] are uti‌lized as a basis in collocation method. Illustrative examples are included to demonstrate the validity and applicability of the techn...

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.

In this paper, we investigate the multifractal decomposition of limit set a finitely generated, free Fuchsian group with respect to mean cusp-winding number. We completely determine its spectrum by means certain energy function and show that Hausdorff dimension sets consisting points same scaling exponent coincides Legendre transform function. As by-product generalize previously obtained result...

Properties of the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known Legendre interpolation operator. The uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. The appl...