Fitted modifications of Runge–Kutta–Nyström pairs of orders 7(5) for addressing oscillatory problems
Vladislav N. Kovalnogov, Maria I. Kornilova, Yuri A. Khakhalev, Dmitry A. Generalov, Theodore E. Simos, Ch. Tsitouras
Abstract
Runge–Kutta–Nyström pair of orders 7(5) using six stages per step have been discovered very recently. Here we modify four of its weights. The resulting method integrates exactly the harmonic oscillator , which serves as model problem. The new weights are perturbations of the original ones. Order reduction which is usually present in such modifications is avoided. Numerical results over standard six stages pairs justify our efforts.
Topics & Concepts
Runge–Kutta methodsMathematicsReduction (mathematics)Harmonic oscillatorOrder (exchange)Applied mathematicsMathematical analysisCalculus (dental)Numerical analysisGeometryPhysicsEconomicsMedicineQuantum mechanicsFinanceDentistryNumerical methods for differential equationsElectromagnetic Simulation and Numerical MethodsMatrix Theory and Algorithms