Solution of One-dimensional Hyperbolic ...

We revisit the cubic B-splines collocation method by investigating its performance in the solution of one-dimensional hyperbolic (eigenvalue and transient elastodynamical) problems. In analogy to the finite element method, we introduce a mass matrix that cooperates with the previously known system matrix, now called stiffness matrix. Following numerical experience gained in 1970s on potential elliptic problems, we show that it is sufficient to use double internal knots (C1-continuity) in conjunction with two collocation points between successive breakpoints. In this way, the number of unknowns becomes equal to the number of equations, which is twice the number of breakpoints. We paid particular attention to the handling of the Neumann boundary conditions. The numerical examples show an excellent quality of the numerical solution. We also found, for the first time, that the cubic B-splines collocation procedure leads to identical results with those obtained using piecewise Hermite collocation.