Adaptive hybridized spline differentiators for numerical solution of the advection equation (Q5903834)

The authors' aim is to develop new numerical differentiation formulas with high accuracy which can be used in the method of lines for partial differential equations. His formulas are derived by approximating the function to be differentiated by suitable splines. Different schemes are set forth and comparison is made in the case of the test equation \(u_ t+vu_ x=0\) with classical difference schemes. The case of nonuniform meshes is also treated. Numerical experiments show the superiority of the method.