Author:

Keywords:

numerical solution, second-order ivps, two-step methods, explicit hybrid methods, oscillating solutions, phase fitting, variable coefficients, runge-kutta methods, numerical-integration, nystrom methods, schrodinger-equation, multistep methods, lag, y''=f(x,y), stability, y), Science & Technology, Technology, Physical Sciences, Computer Science, Interdisciplinary Applications, Physics, Mathematical, Computer Science, Physics, second-order IVPs, RUNGE-KUTTA METHODS, NUMERICAL-INTEGRATION, NYSTROM METHODS, OSCILLATING SOLUTIONS, SCHRODINGER-EQUATION, MULTISTEP METHODS, LAG, Y''=F(X,Y), STABILITY, Y), 01 Mathematical Sciences, 02 Physical Sciences, Fluids & Plasmas, 49 Mathematical sciences, 51 Physical sciences

Abstract:

In this paper a phase-fitted and amplification-fitted explicit two-step hybrid method is introduced. The construction is based on a modification of a fifth-order dissipative method recently developed by Franco. Two free parameters are added in order to nullify the phase-lag and the amplification. Numerical results obtained for well-known test problems show the efficiency of the new method when it is compared with other existing codes.