Software for the Numerical Solution of Nonlocal PDEs

Mark Adams, Paul Muir

Department of Mathematics and Computing Science

Saint Mary’s University

Halifax, N.S., CANADA B3H 3C3

COLNEWSC is an update of the collocation solver COLNEW (available at https://www.netlib.org/ode/colnew.f ). The collocation solution is augmented with a superconvergent (higher accuracy) interpolant based on the use of continuous mono-implicit Runge-Kutta methods. This generally allows COLNEWSC to obtain a numerical solution that meets the user tolerance using a much coarser mesh than would be required by COLNEW, leading to substantial savings in execution time.

User Manual: COLNEWSC_User_Manual (Jan. 2024)

See also: Adams M., Muir P., Differential equation software for the computation of error-controlled

continuous approximate solutions. Numerical Algorithms, 2024 Feb 28:1-24.

Main Package: colnewsc.f90 (Jan. 2024)

Wrapper Package: colnewsc_wrapper.f90 (Jan. 2024)

Auxiliary Linear Algebra Package: dblas.f (Jan. 2024)

To create the executable, use:

gfortran -w colnewsc.f90 colnewsc_wrapper.f90 dblas.f test_problem.f90

where test_problem.f90 is one of the following:

· Swirling flow between two rotating disks (Problem 1.20 from [Asher, Mattheij, Russell, 1995]; also bvpT33 from the Test Set for BVP Solvers) : swf_iii.f90 (Jan. 2024)

· bvpT20 test problem from the Test Set for BVP Solvers: tp20.f90 (Jan. 2024)

· bvpT21 test problem from the Test Set for BVP Solvers: tp21.f90 (Jan. 2024)

· Measles problem (Problem 1.10 from [Asher, Mattheij, Russell, 1995], also available from the Test Set for BVP Solvers): measles.f90 (Jan. 2024)

· Transverse Method-Of-Lines applied to a PDE: tmlpde.f90 (Jan. 2024)

· Shock wave problem (Problem 1.17 from [Asher, Mattheij, Russell, 1995], also bvpT24 from the Test Set for BVP Solvers): swave.f90 (Jan. 2024)

· bvpT4 test problem from the Test Set for BVP Solvers: tp4.f90 (Jan. 2024)

· Example 1 from [Themistoclakis and Vecchio, J. Comput. Appl. Math., 2016]: ThVe16-Ex1.f90 (Jun. 2024)

· Example 1 from [Singh and Wazwaz, Int. J. Appl. Comput. Math., 2022]: SiWa22-Ex1.f90 (Jun. 2024)

· Example 1 from [Singh, Nelakanti, and Kumar, J. Math. Chem., 2014]: SNK14-Ex1.f90 (Jun. 2024)

· Example 2 from [Singh, Nelakanti, and Kumar, J. Math. Chem., 2014]: SNK14-Ex2.f90 (Jun. 2024)

· Example 2 from [Khuri and Wazwaz, J. Math. Chem., 2014]: KhWa14-Ex2.f90 (Jun. 2024)

· Example 4 from [Khuri and Wazwaz, J. Math. Chem., 2014]: KhWa14-Ex4.f90 (Jun. 2024)

Note that COLNEWSC requires that all problems be written in first-order system form, y’(x) = f(x, y(x)), with separated boundary conditions, bR(y(a))=0, bL(y(b))=0.

Last updated June 12, 2024 by Paul Muir