A Fully Implicit Finite Difference Approximation to the One-dimensional Wave Equation using a Cubic Spline Technique

A cubic spline approximation to the wave equation is shown toproduce a fully implicit finite difference representation, themore usual explicit and implicit approximations of this equationbeing shown as special cases of the formulation given here.The truncation error and stability condition are derived forthe scheme produced, and the full computational procedure forthe scheme's solution is developed.