An Explicit Finite Difference Solver by Parameter Estimation
Explicit finite difference schemes are possibly the simplest methods to solve initial value problems. The main drawback, however, is that in order to maintain stability of computation, step size must be small. This often increases computer run time, especailly when steady-state solutions are needed. In ref. , the second author combined a predictor which is an explicit finite difference scheme with a one-step corrector and solved Burgers’ equation given in section 7. The step sizes were chosen such that the stability criterion for the predictor alone was violated. The corrector required estimation of a filtering parameter such that stability properties may be maintained.
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