Asymptotic convergence of cubic Hermite collocation method for parabolic partial differential equation

- Asymptotic convergence of cubic Hermite collocation method for PDEs is established of order 2.
- Zeros of Chebyshev polynomials are used as collocation points.
- Theoretical results are verified for two test problems.

In this paper, the asymptotic convergence of cubic Hermite collocation method in continuous time for the parabolic partial differential equation is established of order Oh2. The linear combination of cubic Hermite basis taken as approximating function is evaluated using the zeros of Chebyshev polynomials as collocation points. The theoretical results are verified for two test problems.