PLTMGC is a program package for solving nonlinear elliptic systems that have explicit dependence on a scalar parameter. In addition to being able to compute solutions for fixed parameter values, it can be used to solve the linear eigenvalue problem, trace solution branches, locate singular points (simple turning points and bifurcation points) and switch branch at simple bifurcation points. A multi-grid continuation approach is employed in which a continuation procedure is used to follow the solution curve on the coarset grid and a multi-grid algorithm is used to refine the solution at selected points using an adaptive mesh refinement strategy. Some numerical examples illustrating the performance of the package are given.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Xie, Ziqing; Yi, Wenfan; Zhou, Jianxin: An augmented singular transform and its partial Newton method for finding new solutions (2015)
  2. Chang, S.-L.; Chien, C.-S.; Jeng, B.-W.: An efficient algorithm for the Schrödinger-Poisson eigenvalue problem (2007)
  3. García-Archilla, Bosco; Sánchez, Juan; Simó, Carles: Krylov methods and determinants for detecting bifurcations in one parameter dependent partial differential equations (2006)
  4. Juncu, Gh.; Mosekilde, E.; Popa, C.: Numerical experiments with MG continuation algorithms (2006)
  5. Moret, I.: A projection method for computing turning points of nonlinear equations (1992)
  6. Kapania, R.K.: A pseudo-spectral solution of 2-parameter Bratu’s equation (1990)
  7. Allgower, Eugene L.; Chien, C.-S.; Georg, Kurt: Large sparse continuation problems (1989)
  8. Giovangigli, V.; Smooke, M.D.: Adaptive continuation algorithms with application to combustion problems (1989)
  9. Szymczak, W.G.; Solomon, J.M.; Berger, A.E.; Bell, J.B.: Multiple discrete solutions of the incompressible steady-state Navier- Stokes equations (1988)
  10. Bank, Randolph E.; Chan, Tony F.: PLTMGC: A multi-grid continuation program for parameterized nonlinear elliptic systems (1986)
  11. Boyd, John P.: An analytical and numerical study of the two-dimensional Bratu equation (1986)
  12. Chan, Tony F.: Techniques for large sparse systems arising from continuation methods (1984)