Second kind Chebyshev polynomial differentiation and integration matrices for solving some mathematical models

In the current work, new pseud-spectral differentiation and integration matrices have been constructed via the second kind of Chebyshev polynomials as a basis function. To achieve that purpose, the continuous inner product of the spectral expansion summation is transformed into a discrete one via the Trapezoidal integration technique. Hence, the given problem, differential, integral, or integro-differential equations, is transformed into a system of algebraic equations. Unlike the standard spectral methods, the algebraic system of equations’ unknowns are the dependent variables’ values at equidistant points. The constructed pseud-spectral differentiation and integration matrices have been tested to approximate the differentiation and integration of known functions to examine their applicability as differentiation and integration operators. In addition, the matrices have been used to approximate the solution of differential, integral equations, and integro-differential equations. Some of the presented differential, integral, and integro-differential equations represent models concerning real-life applications. Log error figures have shown the stability of the results.