Bernoulli Wavelet Collocation Method for the Numerical Solution of Integral and Integro-Differential Equations

Bernoulli wavelet collocation method for the numerical solution of Volterra, Fredholm, mixed Volterra-Fredholm integral and integro-differential equations and !bel's integral equations. The new technique is based upon Bernoulli polynomials, Bernoulli numbers and Bernoulli wavelet approximations. The properties of Bernoulli wavelet is first presented and the resulting Bernoulli wavelet matrices are utilized to reduce the integral and integro-differential equations into system of algebraic equations to get the required Bernoulli coefficients, which are computed by using Matlab. This technique is tested on some numerical examples and compared with the exact and existing methods (i.e., Legendre Wavelet and Hermite Wavelet). Error analysis is worked out, which shows efficiency of the new technique.