Explicit finite-difference methods for nonlinear dynamic systems: Froude's pendulum
Numerical schemes based on first-order methods and a second-order method are developed and analysed for solving the nonlinear Froude's pendulum system. The second-order method is developed by taking a linear combination of three first-order methods. Though implicit in nature, with the resulting improvements in stability, the methods are applied explicitly. These methods are extended to a more general second-order ordinary differential equation. Stability of the numerical methods is approached from the point of view of dynamical systems. lt is found that the methods are stable under the same conditions as those required by the linearized schemes in the neighbourhood of constant, stable, fixed points of the underlying initial-value problem. For the second-order method, this result is found to hold for any chosen value of the step-length.
linear combination of three first-order methods
scientific article; zbMATH DE number 1087156
scientific article