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  2. Numerov's method - Wikipedia

    en.wikipedia.org/wiki/Numerov's_method

    Numerov's method (also called Cowell's method) is a numerical method to solve ordinary differential equations of second order in which the first-order term does not appear. It is a fourth-order linear multistep method. The method is implicit, but can be made explicit if the differential equation is linear.

  3. Second-order cone programming - Wikipedia

    en.wikipedia.org/wiki/Second-order_cone_programming

    The "second-order cone" in SOCP arises from the constraints, which are equivalent to requiring the affine function (+, +) to lie in the second-order cone in +. [ 1 ] SOCPs can be solved by interior point methods [ 2 ] and in general, can be solved more efficiently than semidefinite programming (SDP) problems. [ 3 ]

  4. Second-order arithmetic - Wikipedia

    en.wikipedia.org/wiki/Second-order_arithmetic

    A subsystem of second-order arithmetic is a theory in the language of second-order arithmetic each axiom of which is a theorem of full second-order arithmetic (Z 2). Such subsystems are essential to reverse mathematics , a research program investigating how much of classical mathematics can be derived in certain weak subsystems of varying strength.

  5. Double integrator - Wikipedia

    en.wikipedia.org/wiki/Double_integrator

    Feedback system with a PD controller and a double integrator plant In systems and control theory , the double integrator is a canonical example of a second-order control system. [ 1 ] It models the dynamics of a simple mass in one-dimensional space under the effect of a time-varying force input u {\displaystyle {\textbf {u}}} .

  6. Settling time - Wikipedia

    en.wikipedia.org/wiki/Settling_time

    Settling time depends on the system response and natural frequency. The settling time for a second order , underdamped system responding to a step response can be approximated if the damping ratio ζ ≪ 1 {\displaystyle \zeta \ll 1} by T s = − ln ⁡ ( tolerance fraction ) damping ratio × natural freq {\displaystyle T_{s}=-{\frac {\ln ...

  7. Root locus analysis - Wikipedia

    en.wikipedia.org/wiki/Root_locus_analysis

    The definition of the damping ratio and natural frequency presumes that the overall feedback system is well approximated by a second order system; i.e. the system has a dominant pair of poles. This is often not the case, so it is good practice to simulate the final design to check if the project goals are satisfied.

  8. Step response - Wikipedia

    en.wikipedia.org/wiki/Step_response

    In the case of linear dynamic systems, much can be inferred about the system from these characteristics. Below the step response of a simple two-pole amplifier is presented, and some of these terms are illustrated. In LTI systems, the function that has the steepest slew rate that doesn't create overshoot or ringing is the Gaussian function.

  9. Symplectic integrator - Wikipedia

    en.wikipedia.org/wiki/Symplectic_integrator

    The Verlet method is the second-order integrator with = and coefficients =, =, = =. Since c 1 = 0 {\displaystyle c_{1}=0} , the algorithm above is symmetric in time. There are 3 steps to the algorithm, and step 1 and 3 are exactly the same, so the positive time version can be used for negative time.