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.

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  1. DiPietro, Kelsey L.; Lindsay, Alan E.: Adaptive solution to two-dimensional partial differential equations in curved domains using the Monge-Ampére equation (2019)
  2. Gowrisankar, S.; Natesan, Srinivasan: An efficient robust numerical method for singularly perturbed Burgers’ equation (2019)
  3. Pew, Jack; Li, Zhi; Tannahill, Connor; Muir, Paul; Fairweather, Graeme: Performance analysis of error-control B-spline Gaussian collocation software for PDEs (2019)
  4. Alharbi, Abdulghani; Naire, Shailesh: An adaptive moving mesh method for thin film flow equations with surface tension (2017)
  5. Haynes, Ronald D.; Kwok, Felix: Discrete analysis of domain decomposition approaches for mesh generation via the equidistribution principle (2017)
  6. Esmaeilbeigi, Mohsen; Garmanjani, Gholamreza: A shift-adaptive meshfree method for solving a class of initial-boundary value problems with moving boundaries in one-dimensional domain (2016)
  7. Browne, P. A.; Budd, C. J.; Piccolo, C.; Cullen, M.: Fast three dimensional r-adaptive mesh redistribution (2014)
  8. Liang, Kewei; Zhu, Hancan: Moving collocation method for a reaction-diffusion equation with a traveling heat source (2013)
  9. Muir, Paul H.: B-spline Gaussian collocation software for 1D parabolic PDEs (2013)
  10. Ma, Jingtang; Jiang, Yingjun: Moving collocation methods for time fractional differential equations and simulation of blowup (2011)
  11. Marlow, R.; Hubbard, M. E.; Jimack, P. K.: Moving mesh methods for solving parabolic partial differential equations (2011)
  12. Sulman, Mohamed; Williams, J. F.; Russell, R. D.: Optimal mass transport for higher dimensional adaptive grid generation (2011)
  13. Zhan, Jie-min; Li, Yok-sheung; Dong, Zhi: Chebyshev finite spectral method with extended moving grids (2011)
  14. Budd, C. J.; Williams, J. F.: How to adaptively resolve evolutionary singularities in differential equations with symmetry (2010)
  15. Ata, R.; Soulaïmani, A.; Chinesta, F.: The natural volume method (NVM): Presentation and application to shallow water inviscid flows (2009)
  16. Russell, R. D.; Williams, J. F.; Xu, X.: MOVCOL4: A moving mesh code for fourth-order time-dependent partial differential equations (2007)
  17. Alhumaizi, Khalid: A moving collocation method for the solution of the transient convection-diffusion-reaction problems (2006)
  18. Olmos, Daniel; Shizgal, Bernie D.: A pseudospectral method of solution of Fisher’s equation (2006)
  19. Sarra, Scott A.: Adaptive radial basis function methods for time dependent partial differential equations (2005)
  20. Wang, R.; Keast, P.; Muir, P.: BACOL: B-spline adaptive collocation software for 1-D parabolic PDEs (2004)

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