in this paper‎, ‎based on cas wavelets we present quadrature rules for numerical solution‎ ‎of double and triple integrals with variable limits of integration‎. ‎to construct new method‎, ‎first‎, ‎we approximate the unknown function by cas wavelets‎. ‎then by using suitable collocation points‎, ‎we obtain the cas wavelet coefficients that these coefficients are applied in approximating the unk...

In this paper‎, ‎based on CAS wavelets we present quadrature rules for numerical solution‎ ‎of double and triple integrals with variable limits of integration‎. ‎To construct new method‎, ‎first‎, ‎we approximate the unknown function by CAS wavelets‎. ‎Then by using suitable collocation points‎, ‎we obtain the CAS wavelet coefficients that these coefficients are applied in approximating the unk...

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

In this paper, a new approach to the numerical solution of VolterraFredholm integral equations by using CAS wavelets in combination with the collocation technique is proposed. First, the unknown function is approximated by using CAS wavelets, then the VolterraFredholm integral equation is reduced to the linear or nonlinear system of equations. Moreover, the convergence theorem for the proposed ...

In this paper, a numerical method for solving the Fredholm and Volterra integral equations is presented. The method is based upon the second Chebyshev wavelet approximation. The properties of the second Chebyshev wavelet are first presented and then operational matrix of integration of the second Chebyshev wavelets basis and product operation matrix of it are derived. The second Chebyshev wavel...

Abstract: In this paper, we present a computational method for solving Fredholm-Hammerstein integral equations of the second kind. The method utilizes CAS wavelets constructed on the unit interval as basis in the Galerkin method and reduces the solution of the Hammerstein integral equation to the solution of a nonlinear system of algebraic equations. Error analysis is presented for this method....

This paper presents the application of the Homotopy Analysis Method (HAM) as a numerical solution to linear integro-differential equation. The HAM contains the auxiliary parameter , taht provides a powerful tool to analyze strongly linear and nonlinear problems. Examples are provided to demonstrate the advantages of HAM over the homotopy perturbation method (HPM), sine-cosine wavelets and CAS w...

In this paper, we present a computational method for solving boundary integral equations with logarithmic singular kernels which occur as reformulations of a boundary value problem for Laplace’s equation. The method is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis. This approach utilizes the nonuniform Gauss-Legendre quadrature rule for appr...

Wavelets theory is a relatively new and an emerging area in mathematical research. It has been applied to a wide range of engineering disciplines; particularly, wavelets are very successfully used in signal analysis for wave form representation and segmentations, time frequency analysis and fast algorithms for easy implementation. wavelets permit the accurate representation of a variety of func...