Projection methods for solving urysohn integral equations with multiwavelet bases

Urysohn integral equations appear in many applications,for example it occurs in solving problems arising in economics,engineering and physics. equations of this type have been used to model many thermostatic devices. in this paper the galerkin and the petrov-galerkin methods have been used to solve the nonlinear integral equation of the urysohn type. alpert (1993) constructed a class of wavele bases and applied it to approximate solutions of the fredholm second kind integral equations by the galerkin method. we use alpert multiwavelet bases with orthonormal legendre polynomials to approximate the solution of nonlinear integral equation of the urysohn type. the numerical examples show the good accuracy of the method.