Monotonic scheme of the second order of approximation for the continuous calculation of non-equilibrium flows

In the paper elliptic equations with alternating‐sign coefficients at mixed derivatives are considered. For such equations new difference schemes of the second order of approximation are developed. The proposed schemes are conservative and monotone. The constructed algorithms satisfy the grid maximum principle not only for coefficients of constant signs but also for alternating‐sign coefficients at mixed derivatives. The a prioriestimates of stability and convergence in the grid norm C are obtained.

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Application of Splines of the Second Order Approximation to Volterra Integral Equations of the Second Kind. Applications in Systems Theory and Dynamical Systems

International Journal of Circuits, Systems and Signal Processing ◽

10.46300/9106.2021.15.8 ◽

2021 ◽

Vol 15 ◽

pp. 63-71 ◽

Cited By ~ 2

Author(s):

I. G. Burova ◽

G. O. Alcybeev

Keyword(s):

Dynamical Systems ◽

Systems Theory ◽

Integral Equations ◽

Numerical Experiments ◽

Order Approximation ◽

Second Order ◽

Volterra Integral Equations ◽

Order Of Approximation ◽

Polynomial Splines ◽

Second Order Of Approximation

This paper discusses the application of local interpolation splines of the second order of approximation for the numerical solution of Volterra integral equations of the second kind. Computational schemes based on the use of polynomial and non-polynomial splines are constructed. The advantages of the proposed method include the ability to calculate the integrals which are present in the computational methods. The application of splines to the solution of nonlinear Volterra integral equations is also discussed. The results of numerical experiments are presented

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CONJUGATION PROBLEM ABOUT JOINTLY SEPARATE FLOW OF VISCOELASTIC AND VISCOUS FLUIDS IN THE PLANE DUCT

Mathematical Modelling and Analysis ◽

10.3846/13926292.1999.9637116 ◽

1999 ◽

Vol 4 (1) ◽

pp. 114-123

Author(s):

V. I. Korzyuk ◽

S. V. Lemeshevsky ◽

P. P. Matus ◽

V. N. Shalima

Keyword(s):

Difference Scheme ◽

Separate Flow ◽

Second Order ◽

Viscous Fluids ◽

Spatial Variable ◽

Order Of Approximation ◽

Conjugation Problem ◽

Implicit Difference Scheme ◽

Consistency Conditions ◽

Second Order Of Approximation

Conjugation problem about jointly separate flow of viscoelastic and viscous fluids in the plane duct is considered. The results concerning of solvability of this problem are presented. The implicit difference scheme for the conjugation problem is constructed. The consistency conditions are approximated with the second order of approximation with respect to spatial variable. The convergence of the suggested difference scheme is investigated by method of energy inequalities.

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A Second-Order Approximate Analytical Solution of a Simple Pendulum by the Process Analysis Method

Journal of Applied Mechanics ◽

10.1115/1.2894068 ◽

1992 ◽

Vol 59 (4) ◽

pp. 970-975 ◽

Cited By ~ 48

Author(s):

S. J. Liao

Keyword(s):

Process Analysis ◽

Perturbation Expansion ◽

Expansion Method ◽

Second Order ◽

Order Of Approximation ◽

Analysis Method ◽

Simple Pendulum ◽

Perturbation Expansion Method ◽

Second Order Of Approximation ◽

Perturbation Solutions

In this paper, a new kind of analytical method of nonlinear problem called the process analysis method (PAM) is described and used to give a second-order approximate solution of a simple pendulum. The PAM does not depend on the small parameter supposition and therefore can overcome the disadvantages and limitations of the perturbation expansion method. The analytical approximate results at the second-order of approximation are in good agreement with the numerical results. They are compared with perturbation solutions, and it appears that even the firstorder solutions are more accurate than the perturbation solutions at second-order of approximation.

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