Exact Three-Point Scheme and Schemes of High Order of Accuracy for a Forth-Order Ordinary Differential Equation

2020 ◽  
Vol 56 (4) ◽  
pp. 566-576
Author(s):  
V. Prikazchikov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
High Order ◽  
Order Ordinary Differential Equation ◽  
Order Of Accuracy ◽  
Point Scheme ◽  
High Order Of Accuracy

scholarly journals Well-posedness of the difference schemes of the high order of accuracy for elliptic equations

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Pavel E. Sobolevskiĭ
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Continuous Functions ◽  
High Order ◽  
Difference Schemes ◽  
Well Posedness ◽  
Smooth Functions ◽  
Order Of Accuracy ◽  
High Order Of Accuracy ◽  
The Difference

It is well known the differential equation−u″(t)+Au(t)=f(t)(−∞<t<∞)in a general Banach spaceEwith the positive operatorAis ill-posed in the Banach spaceC(E)=C((−∞,∞),E)of the bounded continuous functionsϕ(t)defined on the whole real line with norm‖ϕ‖C(E)=sup⁡−∞<t<∞‖ϕ(t)‖E. In the present paper we consider the high order of accuracy two-step difference schemes generated by an exact difference scheme or by Taylor's decomposition on three points for the approximate solutions of this differential equation. The well-posedness of these difference schemes in the difference analogy of the smooth functions is obtained. The exact almost coercive inequality for solutions inC(τ,E)of these difference schemes is established.

Numerical methods with a high order of accuracy applied in the quantum system

1996 ◽  
Vol 104 (6) ◽  
pp. 2275-2286 ◽  
Author(s):  
Wusheng Zhu ◽  
Xinsheng Zhao ◽  
Youqi Tang
Keyword(s):  
Numerical Methods ◽  
Quantum System ◽  
High Order ◽  
Order Of Accuracy ◽  
High Order Of Accuracy

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

scholarly journals On the Existence of Eigenmodes of Linear Quasi-Periodic Differential Equations and their Relation to the MHD Continuum

1982 ◽  
Vol 37 (8) ◽  
pp. 830-839 ◽  
Author(s):  
A. Salat
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Infinite Sequence ◽  
Periodic Coefficient ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Magnetic Surfaces ◽  
Toroidal Geometry

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{ω1t, ω2t) is investigated numerically and graphically. For sufficiently incommensurate frequencies ω1, ω2, a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained.The equation considered is a model for the magneto-hydrodynamic “continuum” in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently ir-rational magnetic surfaces

DERIVATION OF 2-POINT ZERO STABLENUMERICAL ALGORITHM OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 5 (2) ◽  
pp. 579-583
Author(s):  
Muhammad Abdullahi ◽  
Bashir Sule ◽  
Mustapha Isyaku
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Order Ordinary Differential Equation ◽  
Differentiation Formula ◽  
First Order ◽  
Backward Differentiation Formula

This paper is aimed at deriving a 2-point zero stable numerical algorithm of block backward differentiation formula using Taylor series expansion, for solving first order ordinary differential equation. The order and zero stability of the method are investigated and the derived method is found to be zero stable and of order 3. Hence, the method is suitable for solving first order ordinary differential equation. Implementation of the method has been considered

A Jupiter Model of Pulsars

1968 ◽  
Vol 1 (4) ◽  
pp. 159-159 ◽  
Author(s):  
R. L. Dowden
Keyword(s):  
Solar System ◽  
Circular Polarization ◽  
High Order ◽  
Radio Sources ◽  
Order Of Accuracy ◽  
Pulsar Period ◽  
High Order Of Accuracy

A precedent to the recently-discovered pulsed radio sources or ‘pulsars’ exists in our own solar system. Jupiter could be thought of as a very slow ‘pulsar’ having a period of about 10 h or 35 000 s. Like pulsars, this emission period is known to a high order of accuracy (about 1 in 106). One difference is that Jupiter emission is received over an appreciable part of this period (1/4 to 1/2 or more) compared with about 1/30 of a typical pulsar period (about 40 ms in 1.3 s). Both pulsar and Jupiter bursts have a microstructure of the order of milliseconds, suggesting similar sizes of instantaneous emission regions. In both, the intensity observed varies from period to period. Emissions from both have relatively strong circular-polarization components at times.

Sign in / Sign up

Export Citation Format

Share Document