Numerical solution of some partial differential equations with Bernoulli wavelet collocation method

In this thesis, some partial differential equations were introduced, and their numerical solutions were obtained using the Bernoulli wavelet collocation method. To employ this method, Bernoulli polynomials were first introduced, and the Bernoulli wavelet family was defined. Subsequently, the integrals of these wavelets were calculated, and the functional matrices of the obtained integrals were derived. Then, with the aid of these matrices, the considered equations were transformed into a system of algebraic equations. The resulting systems were solved using the Maple and Matlab programs. The numerical solutions obtained by applying the Bernoulli wavelet collocation method to the partial differential equations were compared with the exact solutions, and the convergence of the numerical solution to the exact solution was demonstrated through figures. It was observed that the method used provides a good approximation of the numerical solution to the exact solution.