fourth-kind chebyshev computational approach for integro-differential equations

This study proposes a numerical approach for solving integro-differential equations (ides) of the fredholm and volterra types. the method utilizes a collocation computational approach with fourth-kind shifted chebyshev polynomials. by employing this approach, the original ide problem is transformed into a set of linear algebraic equations, which are subsequently solved using the matrix inversion strategy. the proposed method is applied to three numerical instances, and the obtained results are compared with existing literature solutions. the comparison demonstrates the accuracy and effectiveness of the proposed approach. the study presents the results in tables and figures to provide a clear visual representation of the findings.