Journal ArticleDOI
Stabilization of Cowell's classical finite difference method for numerical integration
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This article is published in Journal of Computational Physics.The article was published on 1974-10-01. It has received 64 citations till now. The article focuses on the topics: Finite difference method & Numerical integration.read more
Citations
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P-stable linear symmetric multistep methods for periodic initial-value problems
TL;DR: From the numerical results obtained by the new method to well-known periodic problems, show the superior efficiency, accuracy, stability of the method presented.
Galerkin's Procedure for Nonlinear Periodic Systems (関数方程式の近似解法研究会報告集)
TL;DR: In this paper, it was shown that Galerkin's procedure is always available for twice continuously differentiable periodic differential systems if a periodic solution is restricted to an isolated periodic solution.
Journal ArticleDOI
An explicit sixth-order method with phase-lag of order eight for y ″= f ( t , y )
M. M. Chawla,P S Rao +1 more
TL;DR: In this article, the authors presented a new two-step 6th-order method with phase-lag (1/3 628 800) H8 for numerical integration of periodic initial value problems.
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Mixed collocation methods for y ′′ =f x,y </inline-equatio
TL;DR: The collocation methods introduced in this paper are based on linear combinations of trigonometric functions and powers and provide better approximations for oscillatory solutions of initial-value problems for differential equations of the special form y″=f(x,y).
Journal ArticleDOI
On modified Runge–Kutta trees and methods
TL;DR: The relative theory including a theorem for the generating function of these additional mRK trees is presented and the procedure to determine the extra algebraic equations of condition generated for a major subcategory of these methods is explained.
References
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Journal ArticleDOI
Numerical integration of ordinary differential equations based on trigonometric polynomials
TL;DR: In this article, the authors present a method for the step-by-step integration of periodic or oscillatory solutions where the frequency, or some suitable substitute, can be estimated in advance.
Journal ArticleDOI
Stabilization of Cowell's method
E. Stiefel,D. G. Bettis +1 more
TL;DR: In this article, a modification of the Cowell method for the integration of orbits is proposed, which is characterized by the property that it will integrate unperturbed Kepler motion exactly (without truncation errors), thus the slight instability of the cowell method is avoided.
Journal ArticleDOI
Galerkin's procedure for nonlinear periodic systems
TL;DR: In this paper, it was shown that Galerkin's procedure is always available for twice continuously differentiable periodic differential systems if a periodic solution is restricted to an isolated periodic solution.