High order locally one-dimensional methods for solving two-dimensional parabolic equations. (English) Zbl 1448.65094
Summary: Based on the locally one-dimensional strategy, we propose two high order finite difference schemes for solving two-dimensional linear parabolic equations. In the first method, fourth order approximation in space and \((2,2)\) Padé formula in time are considered. These lead to a fourth order finite difference scheme in both space and time. For the second method, we employ sixth order approximation in space and \((3,3)\) Padé formula in time. This yields a novel sixth order scheme in both space and time. The methods are proved to be unconditionally stable, and the Sheng-Suzuki barrier is successfully avoided. Numerical experiments are given to illustrate our conclusions as well as computational effectiveness.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35K05 | Heat equation |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
Keywords:
parabolic equations; locally one-dimensional strategy; Padé approximations; high order methods; unconditional stabilityReferences:
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