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MOVCOL -- 1D Moving Collocation Method (fortran77)

MOVCOL is primarily intended to solve systems of second-order parabolic PDEs in one space dimension. It is also capable of solving hyperbolic PDEs with suitably smooth solutions. MOVCOL uses a method of lines approach based upon a MOVing COLlocation method. The physical PDEs are discretized in space with a cubic Hermite colloction-type method, and the MMPDEs (moving mesh PDEs) for computing the moving mesh points are discretized with a 3-point finite difference method. The resulting ODE system is integrated in time with the DAE solver DASSL developed by L. Petzold.

For the detailed description of MOVCOL method, see W. Huang and R. D. Russell, A moving collocation method for solving time dependent partial differential equations, Appl. Numer. Math. 20 (1996), 101-116.

Use of MOVCOL will need dlinpk.f (click here) and ddassl.f (click here).

MOVCOL is extended for solving 4th-order PDEs by R. D. Russell, J. F. Williams, and X. Xu, MOVCOL4: A moving mesh code for fourth-order time-dependent partial differential equations, SIAM J. Sci. Comput. 29 (2007), 197-220.

    movcol.f: movcol.f
    example driver for Burgers' equation: ex1.f
    example driver for Dwyer-Sanders flame propagation model (two components): ex2.f
    example driver for a semilinear parabolic PDE with blowup solution: ex3.f
    compute unit round and etc: daux.f
    makefile: makefile
    commands for plotting with gnuplot: plot.1
    commands for plotting with gnuplot: plot.2