A Legendre multiwavelet based method is developed in this paper to solve second kind hypersingular integral equation by converting it into a Cauchy singular integro-differential equation. Multiscale representation of the singular and differential operators is obtained by employing Legendre multiwavelet basis. An estimate of the error of the approximate solution of the integral equation is obtai...

In this paper Legendre wavelet bases have been used for finding approximate solutions to singular boundary value problems arising in physiology. When the number of basis functions are increased the algebraic system of equations would be ill-conditioned (because of the singularity), to overcome this for large $M$, we use some kind of Tikhonov regularization. Examples from applied sciences are pr...

ABSTACT Experimental diiraction pole gure data are thought of as being discretely sampled from pole density functions P(h; r), i.e. even probability density functions deened on the cross-product S 2 S 2 of two unit spheres. Several useful representations of pole density functions exist which are usually related to speciic purposes: (i) series expansion into spherical harmonics, (ii) series expa...

Experimental diffraction pole figure data are thought of as being discretely sampled from pole density functions P(h, r), i.e. even probability density functions defined on the cross-product S2 x S2 of two unit spheres. Several useful representations of pole density functions exist which are usually related to specific purposes: (i) series expansion into spherical harmonics, (ii) series expansi...

In this paper, we present a numerical method for solving Hallen’s integral equation based on radial basis functions (RBFs). This method will represent the solution of Hallen’s integral equation by interpolating the radial basis functions based on Legendre-Gauss-Lobatto(LGL) nodes and weights. The numerical results show that the proposed method for Hallen’s integral equation is very accurate and...

We present a Runge-Kutta discontinous Galerkin (RKDG) method to solve the level set advection equation arising in the conservative level set method. We show results obtained using the method of manufactured solutions demonstrating k + 1 order accuracy for k-th order Legendre polynomial basis functions. The RKDG conservative level set method yields superior results compared to standard finite di...

In this study a numerical method is developed to solve the Hammerstein integral equations. To this end the kernel has been approximated using the leastsquares approximation schemes based on Legender-Bernstein basis. The Legender polynomials are orthogonal and these properties improve the accuracy of the approximations. Also the nonlinear unknown function has been approximated by using the Berns...

In this paper‎, ‎we decide to select the best center nodes‎ ‎of radial basis functions by applying the Multiple Criteria Decision‎ ‎Making (MCDM) techniques‎. ‎Two methods based on radial basis‎ ‎functions to approximate the solution of partial differential‎ ‎equation by using collocation method are applied‎. ‎The first is based‎ ‎on the Kansa's approach‎, ‎and the second is based on the Hermit...

abstract. the main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. properties of the legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. afterwards, an iterative algorithm is examined for solvin...

in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.