The impact of a natural time change on the convergence of the Crank–Nicolson scheme

@inproceedings{Reisinger2012TheIO,
  title={The impact of a natural time change on the convergence of the Crank–Nicolson scheme},
  author={Christian Reisinger and Alan Whitley},
  year={2012}
}
We first analyse the effect of a square root transformation to the time variable on the convergence of the Crank-Nicolson scheme when applied to the solution of the heat equation with Dirac delta function initial conditions. In the original variables, the scheme is known to diverge as the time step is reduced with the ratio of the time step to space step held constant and the value of this ratio controls how fast the divergence occurs. After introducing the square root of time variable we prove… CONTINUE READING

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