An Analytical and Numerical Study of the Two-Dimensional Bratu Equation

@inproceedings{Boyd2004AnAA,
  title={An Analytical and Numerical Study of the Two-Dimensional Bratu Equation},
  author={John P. Boyd},
  year={2004}
}
Bratu's problem, which is the nonlinear eigenvalue equation Au + 2 exp(u)= 0 with u = 0 on the walls of the unit square and 2 as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance of symmett:v: because of invariance under the C 4 rotation group and parity in both x and y, one can slash the size of the basis set by a factor of eight and reduce the CPU time by three orders of magnitude. Second, the pseudospectral… CONTINUE READING
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References

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Showing 1-7 of 7 references

PLTMGC : A multigrid continuation program for parameterized nonlinear elliptic systems

  • G. Birkhoff, R. E. Lynch
  • SlAM J . Sei . Stal . Comp .
  • 1986

The efficient solution of Poisson ' s equation in two dimensions via Chebyshev approximation

  • D. B. Haidvogel, T. Zang
  • J . Comp . Phys .
  • 1979

Spectral and pseudospectral methods for eigenvalue and nonseparable boundary value problems

  • P. BoydBoyJ.
  • Mon . Wea . Rev .
  • 1978

Polynomial series versus sinc expansions for functions with corner or endpoint singularities

  • J. P. Boyd
  • J . Comp . Phys .

Solitons from sine waves : Analytical and numerical methods for nonintegrable solitary and sinoidal waves

  • J. P. Boyd

Spectral methods using rational basis functions on an infinite interval

  • J. P. Boyd

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