Journal ArticleDOI
Numerical Integration of Ordinary Differential Equations
TLDR
In this article, the integration of Ordinary Differential Equations (ODE) has been studied in the context of algebraic geometry, and it has been shown that it is possible to integrate ODEAbstract:
(1926). Numerical Integration of Ordinary Differential Equations. The American Mathematical Monthly: Vol. 33, No. 9, pp. 455-460.read more
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Journal ArticleDOI
Stability of a Numerical Solution of Differential Equations
W. E. Milne,R. R. Reynolds +1 more
TL;DR: It is shown that the occasional application of Newton's “three eighths” quadrature formula over three intervals can effectively damp out the unwanted oscillation without harm to the desired solution.
Journal ArticleDOI
Construction of variable-stepsize multistep formulas
TL;DR: In this paper, a general fixed-step-size multistep formula was extended to a minimum storage variable step-size formula, which encompasses fixed-coefficient (interpolatory), variable-step (variable step), and fixed leading coefficient as special cases.
Journal ArticleDOI
Formulation and Implementation of Nonlinear Integral Equations to Model Neural Dynamics Within the Vertebrate Retina.
Jason K. Eshraghian,Seungbum Baek,Jun-Ho Kim,Nicolangelo Iannella,Kyoung-Rok Cho,Yong Sook Goo,Herbert Ho-Ching Iu,Sung-Mo Steve Kang,Kamran Eshraghian +8 more
TL;DR: This research presents a novel approach that requires the effective integration of different dynamical time scales within a unified framework of neural responses, where the rod, cone, amacrine, bipolar, and ganglion cells correspond to the implemented pathways.
Journal ArticleDOI
High order stiffly stable composite multistep methods for numerical integration of stiff differential equations
Theodore A. Bickart,Zdenek Picel +1 more
TL;DR: In this article, the Lagrange interpolating polynomial (LIP) method is used to obtain the approximate solution at only one past point in each component multistep formula of the method and the local truncation error for the first component multi-step formula is easily evaluated as
Journal ArticleDOI
Trigonometrically-fitted second derivative method for oscillatory problems
TL;DR: The stability properties of the TSDM are discussed and numerical experiments are presented to demonstrate the efficiency of the method.