A universal centred high-order method based on implicit Taylor series expansion with fast second order evolution of spatial derivatives

In this paper, a centred universal high-order finite volume method for solving hyperbolic balance laws is presented. The scheme belongs to the family of ADER methods where Generalized Riemann Problems (GRP) building block. solution these problems carried through an implicit Taylor series expansion, which allows works very well stiff source terms. A von Neumann stability analysis out investigate range CFL values and accuracy are balanced. implements centred, low dissipation approach dealing with advective part system profits from small values. Numerical tests demonstrate that present can solve, efficiently, in both conservative non-conservative form as well. An empirical convergence rate assessment shows expected theoretical orders achieved up fifth order.