A Comparison of Analytical Solutions of a High-Order RBC Scheme and Its Equivalent Differential Equation for a Steady Shock Problem

2014 ◽  
pp. 169-183
Author(s):  
Alain Lerat
Keyword(s):  
Differential Equation ◽  
Analytical Solutions ◽  
High Order ◽  
Steady Shock

scholarly journals On Runge-Kutta processes of high order

1964 ◽  
Vol 4 (2) ◽  
pp. 179-194 ◽  
Author(s):  
J. C. Butcher
Keyword(s):  
Differential Equation ◽  
High Order ◽  
Runge Kutta ◽  
Image Position

An (explicit) Runge-Kutta process is a means of numerically solving the differential equation , at the point x = x0+h, where y, f may be vectors.

scholarly journals Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Essam R. El-Zahar
Keyword(s):  
Asymptotic Expansion ◽  
Singular Perturbation ◽  
Analytical Solutions ◽  
Source Term ◽  
High Order ◽  
Singular Perturbation Problems ◽  
Weakly Coupled System ◽  
Approximate Analytical Solutions ◽  
Discontinuous Source Term ◽  
Perturbation Problems

A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and Differential Transform Method (DTM). First, the original problem is transformed into a weakly coupled system of ODEs and a zero-order asymptotic expansion of the solution is constructed. Then a piecewise smooth solution of the terminal value reduced system is obtained by using DTM and imposing the continuity and smoothness conditions. The error estimate of the method is presented. The results show that the method is a reliable and convenient asymptotic semianalytical numerical method for treating high-order singular perturbation problems with a discontinuous source term.

scholarly journals On Conjugacy of High-Order Linear Ordinary Differential Equations

1994 ◽  
Vol 1 (1) ◽  
pp. 1-8
Author(s):  
T. Chanturia
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
High Order ◽  
Summable Function ◽  
Order Linear ◽  
Linear Ordinary Differential Equations

Abstract It is shown that the differential equation u (n) = p(t)u, where n ≥ 2 and p : [a, b] → ℝ is a summable function, is not conjugate in the segment [a, b], if for some l ∈ {1, . . . , n – 1}, α ∈]a, b[ and β ∈]α, b[ the inequalities hold.

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