On The Numerical Methods Based On Chebyshev Wavelets For The Non-linear Fredholm-Volterra Integral Equation

Integral equation is the study of mathematics and physics problems often seen in theequation is an important mathematical tool, in practice many problems can betransformed into integral equations to solve. For example, the differential equation canbe transformed into a specific initial conditions to calculate the integral equation.Integral equations usually do not have exact solutions in general, the bestapproximation find its approximate numerical solution, this time integrating the resultsof the relative error caused smaller and more precise. If the shift differential for theintegral equation on the interval, its dimensions will reduce the amount of computationis reduced. So Numerical Solution of Integral Equation of great significance.Background wavelet theory paper summarizes the early wavelet and the currentdevelopment of the full text of the organizational structure introduced from thebeginning of Fourier analysis, introduces the basic theory of wavelet analysis,including the contents of the continuous wavelet, orthogonal wavelet and waveletfunction and so on. In this paper, the integral equation made a detailed presentation,including contact classification integral equations, integral equations and algebraicequations, with emphasis on the use of the basic theory of Chebyshev wavelet solutionof nonlinear Fredholm-Volterra integral equations and nonlinear fractionalFredholm-Volterra integral equation, first integration interval normalized to generateChebyshev collocation points, the interval discrete, so it will generate a Chebyshevwavelet functions into a unified grid matrix algebra, then the use of successiveapproximation method and the results obtained by the wavelet transform. Numerical examples illustrate the feasibility of this method and has high accuracy, and Haarwavelet and Legendre wavelet are compared, the results show that the method has thesimplicity, small high precision computational advantages. This paper also Chebyshevwavelet solution of nonlinear Fredholm-Volterra integral equation problems Fractionalmade a preliminary exploration Chebyshev wavelet format derived nonlinearFredholm-Volterra integral equations, and using successive approximation method forsolving matrix form.