Higher-order variable-step algorithms adapted to the accurate numerical integration of perturbed oscillators
نویسندگان
چکیده
منابع مشابه
Two-step hybrid methods adapted to the numerical integration of perturbed oscillators
Two-step hybrid methods specially adapted to the numerical integration of perturbed oscillators are obtained. The formulation of the methods is based on a refinement of classical Taylor expansions due to Scheifele [Z. Angew. Math. Phys., 22, 186–210 (1971)]. The key property is that those algorithms are able to integrate exactly harmonic oscillators with frequency ω and that, for perturbed osci...
متن کاملVariable Step Implicit Numerical Integration of Stiff Multibody Systems
This paper presents a variable step size implicit numerical integration algorithm for dynamic analysis of stiff multibody systems. Stiff problems are very common in real world applications, and their numerical treatment by means of explicit integration is cumbersome or infeasible. Until recently, implicit numerical integration of the equations of motion of stiff mechanical systems has been prob...
متن کاملHigher-order accurate numerical solution of unsteady Burgers' equation
Higher-order accurate finite-difference schemes for solving the unsteady Burgers’ equation which often arises in mathematical modeling used to solve problems in fluid dynamics are presented. The unsteady Burgers’ equation belongs to a few nonlinear partial differential equations which has an exact solution, and it allows one to compare the numerical solution with the exact one, and the properti...
متن کاملA Runge-Kutta-Nyström pair for the numerical integration of perturbed oscillators
New Runge–Kutta–Nyström methods especially designed for the numerical integration of perturbed oscillators are presented in this paper. They are capable of exactly integrating the harmonic or unperturbed oscillator. We construct an embedded 4(3) RKN pair that is based on the FSAL property. The new method is much more efficient than previously derived RKN methods for some subclasses of problems....
متن کاملA Modified Energy Balance Method to Obtain Higher-order Approximations to the Oscillators with Cubic and Harmonic Restoring Force
This article analyzes a strongly nonlinear oscillator with cubic and harmonic restoring force and proposes an efficient analytical technique based on the modified energy balance method (MEBM). The proposed method incorporates higher-order approximations. After applying the proposed MEBM, a set of complicated higher-order nonlinear algebraic equations are obtained. Higher-order nonlinear algebra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers in Physics
سال: 1998
ISSN: 0894-1866
DOI: 10.1063/1.168717