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

  title={An Analytical and Numerical Study of the Two-Dimensional Bratu Equation},
  author={John P. Boyd},
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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