here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with the unknown Taylor coefficients. Also, we test the ...

in this paper, the two-dimensional triangular orthogonal functions (2d-tfs) are applied for solving a class of nonlinear two-dimensional volterra integral equations. 2d-tfs method transforms these integral equations into a system of linear algebraic equations. the high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

alternative legendre polynomials (alps) are used to approximate the solution of a class of nonlinear volterra-hammerstein integral equations. for this purpose, the operational matrices of integration and the product for alps are derived. then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. the error analysis of the method is given an...

This article analyzes a strongly nonlinear oscillator with cubic and harmonic restoring force and proposes an efficient analytical technique based on the modified energy balance method (MEBM). The proposed method incorporates higher-order approximations. After applying the proposed MEBM, a set of complicated higher-order nonlinear algebraic equations are obtained. Higher-order nonlinear algebra...

the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

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 ...

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then util...

The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...

It is the purpose of this paper to introduce a computer software that is developed for the analysis of general multi degree of freedom rotor bearing systems with non-linear support elements. A numerical-analytical method for the prediction of steady state periodic response of large order nonlinear rotor dynamic systems is addressed which is based on the harmonic balance technique. By utilizing ...