Three-level techniques for one-dimensional parabolic equation with nonlinear initial condition. (English) Zbl 1048.65082
Summary: A boundary value problem for one-dimensional heat equation is considered under the constraint of a nonlocal initial condition. In place of the classical specification of initial data, we impose a nonlocal initial condition. Efficient higher-order algorithms are developed for solving this parabolic partial differential equation with nonstandard initial condition. Several three-level finite difference schemes are presented. These schemes are based on the modification of the centred-time centred-space explicit formula, the three-level (1,3,1) explicit technique, the sixth-order (1,3,3) explicit method and the Dufort-Frankel finite difference scheme. Numerical computations combined with a simple iteration procedure of some examples are given to demonstrate the efficiency and accuracy of the new algorithms.
MSC:
| 65M06 | Finite difference 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 |
Keywords:
Three-level finite difference schemes; Nonlocal time weighting initial condition; Parabolic partial differential equations; Numerical examples; Error bounds; Heat equation: Dufort-Frankel finite difference scheme; AlgorithmsReferences:
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