A new operational matrix of derivative for hybrid third kind Chebyshev polynomials and Block-pulse functions and its applications in solving second-order differential equations

Abstract

In this paper, first, a numerical method is presented for solving generalized linear and nonlinear second-order two point initial and boundary value problems. The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions. The obtained operational matrix is used to reduce the linear or nonlinear equations with their initial or boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. Finally, the efficiency of the proposed method is indicated by some numerical examples.