B-Spline Collocation

The simple advection equation, ut + ux = 0, is solved with initial condition shown, using fourth-order Runge Kutta time advancement and a B-spline collocation method for numerical evaluation of the spatial derivatives. The principal objective is demonstrate the B-spline method and point out certain attractive features it has. B-splines, where the B stands for nothing grander than basis, offer in a sense maximum continuity with minimal support. Support here is quantified by the number of discrete intervals they span. Thus, the 0th order B-spline is a simple box function presented.