[PDF] Top 20 On The Numerical Solution of Urysohn Integral Equation Using Chebyshev Polynomial

... the integral equation, ( ) is the unknown ...this equation are assumed to be continuous and the case of is ...nonlinear integral equations with constant integration ...nonlinear ... See full document

... shifted Chebyshev Polynomials of second ...shifted chebyshev polynomials of second kind denoted by U n ∗ (x) for all x ∈ [0, 1] by change of variable s = 2x − 1 or x = 1/2(s + 1),thus we can write U n ∗ (x) ... See full document

... the Chebyshev polynomial-based differential quadrature method to the solution of a fractional-order Riccati differential ...differential equation to a system of algebraic equations. We present ... See full document

... The numerical results that are obtained using this method converges to the exact solution as the number of Chebyshev polynomial increases, that will be used as a trial function; and ... See full document

... the numerical solution of singular integral equations by using Chebyshev polyno- mials of first, second, third and fourth kind to obtain systems of linear algebraic equations, these ... See full document

... Wavelets were first applied in geophysics to analyze data from seismic surveys, which are used in oil and mineral exploration to get "pictures" of layering in the subsurface rock [13]. There are several bases for ... See full document

... of Equation (7), we represent the linear term ϑ ( ) ℵ , t from Equation (8) and the nonlinear term γ η ζ ϑ η ζ ( , , ( , ) ) will be represented by the He’s polynomials from Equation (10) and ... See full document

... second function of both variables) for some m ≥ 0, 0 < ν ≤ 1, and they are approximated by a finite Chebyshev series of order M . Moreover, for sufficiently large value of M, the homogeneous equation ... See full document

... difference (FDM), finite element (FEM) needs generation of a regular mesh in the domain of the problem which is computationally expensive [1, 2, 3, 4, 5]. During the last decade, mesh- less methods have received much ... See full document

... [19] Sohrabi S. 2011. Comparison Chebyshev wavelet method with BPFs method for solving Abel’s integral equation. Ain Shams Engineering Journal. 2: 249-254. [20] Li Y. 2011. Solving a nonlinear ... See full document

... As shown by numerical examples, the method in- troduced here can be simply implemented to gen- eral nonlinear integral equations of the second kind. The advantages are much less implemen- tations and fast ... See full document

... mixed integral equation of the first kind of type Fredholm- Volterra in position and time, ...Fredholm integral term is considered in a variable position, in the space L 2 [  1 , 1 ] , and has a ... See full document

... Hammerstein integral equations of both Fredholm as well as Volterra type by Chebyshev wavelet method which is widely applicable in engineering and ...The Chebyshev wavelets together its properties ... See full document

... For nonlinear determinate Volterra integral equations, Maleknejad et al. [8] and Nemati et al. [6] used two-dimensional block pulse functions and Legendre polynomials to solve those respectively. Both Babolian et ... See full document

... the solution of a n×n algebraic eigenvalue ...the numerical methods to solve (1) is to reduce it approximately to an algebraic ...the solution is taken to be the approximate solution of ...The ... See full document

... scaling and wavelet functions make wavelet method more efficiently than other methods such as spline ap- proximations in solving an equation. A lot of computa- tional time and storage capacity can be saved since ... See full document

... In this research, a new and robust algorithm is proposed for the optimal control problems. The proposed method is a hybrid second kind Chebyshev and wavelet function which has good characteristics of both ... See full document

... en’s integral equation for mod- eling of radiation from the dipole ...en’s integral equation is solved by the proposed method to obtain the current density on the antenna and its radiation ... See full document

... The present method is verified with some numerical experiments which have been de- scribed in [4, 16, 17]. It is worth noting that the problems are solved on a bounded interval which is uniformly discretized. The ... See full document

... a) Suppose that a ball of mass m starts from rest at time t=0 at the initial point at surface and slides downhole along the above wellbore curve under the action of gravity without friction, neglecting the buoyancy ... See full document