numerical solution of the forced duffing equations‎ ‎ using legendre multiwavelets

Numerical solution of the forced Duffing equations‎ ‎ using Legendre multiwavelets

‎A numerical technique based on the collocation method using Legendre multiwavelets are‎ ‎presented for the solution of forced Duffing equation‎. ‎The operational matrix of integration for ‎Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation‎ ‎to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate‎ ‎the valid...

Numerical Solution of Functional Differential Equations using Legendre Wavelet Method

In this paper, the objective is to solve the functional differential equations in the following form using Legendre Wavelet Method (LWM), 0 f 0 u(t)=f(t ,u( t) ,u( (t))), t t t u( t)= (t), t t ′ α ≤ ≤   φ ≤  (1) where ƒ: [t0, tƒ]×R→R is a smooth function, α(t) is a continuous function on [t0, tƒ] and φ(t)∈C represents the initial point or the initial data. In the present paper, the most impo...

Numerical solution of nonlinear Hammerstein integral equations by using Legendre-Bernstein basis

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...

Legendre polynomials for numerical solution of linear fuzzy Fredholm integral equations

Numerical solution of nonlinear integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions

In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of...

Numerical Solution of Interval Volterra-Fredholm-Hammerstein Integral Equations via Interval Legendre Wavelets ‎Method‎

In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examp...