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This is for a highlight of the application-oriented numerical computation and optimization-a celebration of 60 years of the IJCM publication. On a usual rainy day in early May 1964, the first issue of the International Journal of Computer Mathematics (IJCM) was published in London, Great Britain. Apparently, mathematicians around the world felt and were excited by the morningtide and shock waves from digital computations, after the success of modern computer hardware configuration and software structures. The twilight of the digital new age inspired the pioneers, and this also led to the birth of the IJCM, even before the invention of the word numerical analysis. The first volume of the IJCM consisted of 4 issues, 314 pages of 16 peer-reviewed research papers, and 4 book reviews. 

This study reported the application of an interactive Open Education Resource, namely, an open virtual experiment simulator education tool (OVESET), in teaching the kinetics of atom transfer radical polymerization (ATRP) in a polymer science classroom. The OVESET ATRP kinetic simulator aims at improving students’ inductive reasoning skills. Students were encouraged to perform virtual experiments to systematically examine the influence of each parameter, e.g., type of polymerization and concentrations of reagents, and to observe and make logical explanations of the general trends behind each series of experiments. The tool was designed to maximize accessibility and flexibility through open licensing. The simulator runs under the Jupyter Notebook environment, which is free to use, modify, and redistribute; therefore, instructors can adapt the simulator based on their teaching contexts. The simulator can be applied in a classroom setting without requiring any software installation and can be used across different operating systems. Assessment of the implementation demonstrated that students’ learning outcomes and STEM and polymer science identity were improved. Students also rated the tool as useful in increasing their understanding and inductive reasoning. The quick and in-place response of the notebook makes it ideal for both in-class demonstrations and after-class practices. The tool is freely available at https://bit.ly/ATRP-Simulator. 

For control problems with control constraints, a local convergence rate is established for an hp-method based on collocation at the Radau quadrature points in each mesh interval of the discretization. If the continuous problem has a sufficiently smooth solution and the Hamiltonian satisfies a strong convexity condition, then the discrete problem possesses a local minimizer in a neighborhood of the continuous solution, and as either the number of collocation points or the number of mesh intervals increase, the discrete solution convergences to the continuous solution in the sup-norm. The convergence is exponentially fast with respect to the degree of the polynomials on each mesh interval, while the error is bounded by a polynomial in the mesh spacing. An advantage of the hp-scheme over global polynomials is that there is a convergence guarantee when the mesh is sufficiently small, while the convergence result for global polynomials requires that a norm of the linearized dynamics is sufficiently small. Numerical examples explore the convergence theory. 

A Gauss collocation method is developed for solving optimal control problems with convex control constraints. The method has a local exponential convergence rate when the solution of the continuous problem is smooth and the Hamiltonian possesses a convexity property.