Numerical solution of integro-differential equations of high order by wavelet basis, its algorithm and convergence analysis

Abstract

This paper presents, for the first time, numerical solutions for this particular type of integro-differential equations. According to equations which will be introduced, suitable wavelet Galerkin method is provided using wavelet basis in the space C α ( R ) ⋂ L 2 ( R ) , α > 0 , that C α ( R ) is the Hölder space of exponent α . This approach has two advantages. First, the wavelets basis are arbitrary. It means that any differentiable wavelets basis can be used. Second, the desired orders for this equation are the reasons for involving a wide variety of these types of equations. The Algorithm and convergence analysis of this scheme are described. Numerical examples, plots and tablets of errors confirm the applicability and the validity of the proposed method.