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

作者：Babaaghaie A; Maleknejad K^*

来源：Journal of Computational and Applied Mathematics, 2017, 325: 125-133.

DOI：10.1016/j.cam.2017.04.035

• Fredholm integro-differential equation
• Wavelet Galerkin method
• Wavelets basis
• Convergence analysis

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-alpha (R) boolean AND L-2(R), alpha > 0, that C-alpha (R) is the Holder space of exponent alpha. 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.

• 出版日期2017-12-1