Phase‐fitted, six‐step methods for solving x′′  =  f(t,x)

Abstract

An explicit, six‐step method of sixth order is presented and tuned for the numerical solution of x′′ = f(t,x). This method is explicit, hybrid, and uses two function evaluations (stages) per step. Its coefficients are varied and depend on the step size. This variance comes from the demand of the method to nullify the phase errors produced when solving the standard simple oscillator. The first and second derivative of this error vanish also. Numerical tests in a set of relevant problems illustrate the efficiency of the newly derived method.

Explicit fiber element and its application to piers under multipulse near‐fault earthquake motion

“…[21,22] The phenomenon of wave propagation inside the structure is also studied based on the theory of Timoshenko beam, and the comparison with the experimental results is conducted as well. [23,24] The elastic investigated lump method [6,25] decomposes structure/media into elastic lumps, and the structural/media dynamic response is computed in the time domain. This method is one kind of the propagation-based method, and the transient dynamic responses of the structure/media are analyzed explicitly.…”