Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems. (English) Zbl 1513.65230
Summary: We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation matrices (D-matrices). Those matrices have been used to approximate the solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be used in this work. The first technique is a direct approximation of the H-ODE. While the second technique depends on transforming the H-ODE into a system of lower order ODEs. We discuss the error analysis of these D-matrices in-depth. Also, the approximation and truncation error convergence have been presented to improve the error analysis. Some numerical test functions and examples are illustrated to show the constructed D-matrices’ efficiency and accuracy.
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 33C47 | Other special orthogonal polynomials and functions |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 76M22 | Spectral methods applied to problems in fluid mechanics |
Keywords:
monic Chebyshev polynomials; pseudospectral differentiation matrices; convergence and error analysis; higher-order IVPs and BVPs; MHD; COVID-19References:
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