Application of Bernoulli wavelet method for numerical solution of fuzzy linear Volterra-Fredholm integral equations

  • Mohamed A Ramadan Menoufia University
  • Mohamed R. Ali Benha University
Keywords: Bernoulli polynomials, Bernoulli wavelets, Volterra-Fredholm fuzzy integral equations, Integration of the cross product, Product matrix, Coefficient matrix


This work, Bernoulli wavelet method is formed to solve nonlinear fuzzy Volterra-Fredholm integral equations. Bernoulli wavelets have been Created by dilation and translation of Bernoulli polynomials. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, and then we used it to transform the integral equations to the system of algebraic equations. We compared the result of the proposed method with the exact solution to show the convergence and advantages of the new method. The results got by present wavelet method are compared with that of by collocation method based on radial basis functions method. Finally, the numerical examples explain the accuracy of this method.

Author Biographies

Mohamed A Ramadan, Menoufia University

Department of Mathematics, Faculty of Science, Menoufia University, Egypt

Mohamed R. Ali, Benha University

Department of Mathematics, Faculty of Engineering, Benha University, Egypt