Sub-domain precise integration compact implicit scheme with high accuracy for solving four order parabolic equation. (English) Zbl 1147.65067
Summary: Based on sub-domain precise integration method, an unconditional stable compact scheme containing a parameter \(\alpha > 0\) for solving the periodic initial value problem of a fourth order parabolic equation is presented. The local truncation error is
\[ O ((\Delta t)^2+\alpha(\Delta t)^2 + (\Delta x)^6). \]
The numerical example shows that the scheme constructed in this paper is effective and correct in theoretical analysis.
\[ O ((\Delta t)^2+\alpha(\Delta t)^2 + (\Delta x)^6). \]
The numerical example shows that the scheme constructed in this paper is effective and correct in theoretical analysis.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35K30 | Initial value problems for higher-order parabolic equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
