# Variable-step Variable-order 3-stage Hermite-birkhoff Ode Solver of Order 5 to 15

@inproceedings{NguyenBaVariablestepV3, title={Variable-step Variable-order 3-stage Hermite-birkhoff Ode Solver of Order 5 to 15}, author={Truong Nguyen-Ba and Hemza Yagoub and R{\'e}mi Vaillancourt} }

Variable-step variable-order 3-stage HermiteBirkhoff (HB) methods HB(p)3 of order p = 5 to 15 are constructed for solving non-stiff differential equations. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads to multistep and RungeKutta type order conditions which are reorganized into linear confluent Vandermonde-type systems of HB type. Fast algorithms are developed for solving these systems in O(p) operations to obtain HB interpolation… CONTINUE READING