Numerical approach for the solution of hypersingular integro-differential equations

The main purpose of this article is to present an approximation method of hypersingular integro-differential equations in the most general form under the mixed conditions in terms of the second kind Chebyshev polynomials. This method transforms mixed hypersingular integro-differential equations and the given conditions into matrix equation which corresponding to a system of linear algebraic equation. The error analysis and convergence for the proposed method is also introduced. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system Maple10.