Abstract With the motivation of avoiding the computation of the inverse of Jacobian matrix, which is involved in Newton’s method, we consider the use of vector divisions in solving a nonlinear system of equations F (x) = 0. Vector divisions are applied to form the secant method formulas. Based on that, a globally convergent hybrid algorithm for solving the nonlinear system of equations is propo...

A bst ract : Based on the T-S model ,the output regulation of nonlinear singularly perturbed systems via state feedback is dis2 cussed. It is shown that , under standard assumptions ,this problem is solvable if and only if certain linear matrix equations are solv2 able. Once these equations are solvable , the state feedback regulator can easily be constructed. Keywor ds : Nonlinear systems ; Ou...

Iterative algorithms for solving a system of nonlinear algebraic equations (NAEs): Fi(x j) = 0, i, j= 1,. . . ,n date back to the seminal work of Issac Newton. Nowadays a Newton-like algorithm is still the most popular one to solve the NAEs, due to the ease of its numerical implementation. However, this type of algorithm is sensitive to the initial guess of solution, and is expensive in terms o...

Abstract This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Taylor expansion coefficients, s...

sufficient conditions are established under which the zero solution x = 0 of equation (2) isunstable.

solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modi ed korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

An analogue of Banach’s fixed point theorem in partially ordered sets is proved in this paper, and several applications to linear and nonlinear matrix equations are discussed.

This article points out that the differential quadrature (DQ) and differential cubature (DC) methods, due to their global domain property, are more efficient for nonlinear problems than the traditional numerical techniques such as finite element and finite difference methods. By introducing the Hadamard product of matrices, we obtain an explicit matrix formulation for the DQ and DC solutions of...

This paper generalizes to the nonlinear case a standard way to solve general sparse systems of linear equations. In particular, Duu 1977] has suggested that row and column interchanges be applied to permute the coeecient matrix of a linear system into block lower triangular form. The linear system then can be solved by using the associated block Gauss-Seidel or forward block substitution scheme...

this paper evaluates a new and simple controller design method based on qft (quantitative feedback theory) for a two-link manipulator whose first link is rigid and the second is flexible. a piezoelectric patch is attached to the surface of the flexible link for vibration suppression of it. this system is modeled as a nonlinear multi-input multi-output (mimo) control systems whose inputs are two...