Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems

Abstract We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in (D-matrices). Those have been to approximate solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be this work. The first technique is a direct approximation H-ODE. While second depends transforming H-ODE into system lower order ODEs. discuss error analysis these D-matrices in-depth. Also, and truncation convergence presented improve analysis. Some numerical test examples are illustrated show constructed D-matrices’ efficiency accuracy.