An unconditionally stable compact approximation of order (2,6) for time-dependent reaction-diffusion equation via additive parameters technique
Abstract
We deliberate a new 3 time-level implicit approximation of order (2,6) for the approximate solution of time-dependent linear reaction-diffusion equation. With the support of modified equation approach, additive parameter technique, we show that the proposed approximation is unconditionally stable. The scheme is tri-diagonal in nature and can be computed directly at every advanced time-level. We briefly discuss an approximation of order (2,6) at first time-level. Numerical results are computed with the results of existing methods. The numerical results show that the recommended approximation becomes sixth-order accurate in space.
Fields of Study & Subjects
Differential Equations and Numerical Methods
Advanced Numerical Methods in Computational Mathematics
Numerical methods for differential equations
Publication details
- Journal / source
- Examples and Counterexamples
- Volume
- 9
- Pages
- 100215–100215
- Publication date
- 24 February 2026
- Language
- EN