We investigate local convergence of an SQP method for non-linear optimal control of weakly singular Hammerstein integral equations. Suucient conditions for local quadratic convergence of the method based are discussed.

in this paper, we will compare a homotopy perturbation algorithm and taylor series expansin method for a system of second kind fredholm integral equations. an application of he’s homotopy perturbation method is applied to solve the system of fredholm integral equations. taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

We show that many of Ramanujan’s modular equations of degree 3 can be interpreted in terms of integral ternary quadratic forms. This way we establish that for any n ∈ N

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...

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.

Abstract We study an asymptotic formula for counting integral points over equation defined by a non-degenerate indefinite ternary quadratic form f representing non-zero integer such that $-a\cdot det(\,f)$ is square number field. In particular, we prove the leading coefficient of this given product local densities normalized $1-p^{-1}$ all finite primes p.