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.
"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." Tbilisi Math. J. 14 (1) 163 - 179, March 2021. https://doi.org/10.32513/tmj/19322008113