Abstract
In this paper, we propose a new two-level implicit method of order two in time and four in space directions, based on spline in tension approximation for the numerical solution of one space dimensional quasi-linear parabolic partial differential equation on a uniform mesh. We have discussed the derivation of the proposed method in detail and have also discussed the stability analysis for a model problem. We have extended the method to non-uniform mesh. Numerical results are given to illustrate the usefulness of the proposed methods.
Acknowledgements
The authors thank the reviewers for their valuable suggestions, which substantially improved the standard of the paper.
Disclosure Statement
No potential conflict of interest was reported by the authors.