A new Bernoulli wavelet method for accurate solutions of nonlinear fuzzy Hammerstein-Volterra delay integral equations

In this article, Bernoulli wavelet method has been developed to solve nonlinear fuzzy Hammerstein-Volterra integral equations with constant delay. This type of integral equation has a particular case the fuzzy variant of a mathematical model from epidemiology. Bernoulli wavelets have been generated by dilation and translation of Bernoulli polynomials. The properties of Bernoulli wavelets and Bernoulli polynomials are first presented. The present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by Newton's method. Convergence analysis of the present method has been discussed in this article. Also the results obtained by present wavelet method have been compared with that of by B-spline wavelet method. Some illustrative examples have been demonstrated to show the applicability and accuracy of the present method.