A COMPARISON OF NUMERICAL SCHEMES TO CALCULATE THE SOLUTIONS OF A NON- LINEAR PARTIAL DIFFEREN TIAL EQUATION WITH SHOCKS

1963 ◽  
Author(s):  
A. Douglis
Keyword(s):  
Numerical Schemes ◽  
Differen Tial Equation ◽  
Non Linear

scholarly journals On Computer Implementation for Comparison of Inverse Numerical Schemes for Non-Linear Equations

2021 ◽  
Vol 36 (3) ◽  
pp. 493-507
Author(s):  
Mudassir Shams ◽  
Naila Rafiq ◽  
Nazir Ahmad Mir ◽  
Babar Ahmad ◽  
Saqib Abbasi ◽  
...  
Keyword(s):  
Linear Equations ◽  
Computer Implementation ◽  
Numerical Schemes ◽  
Non Linear ◽  
Non Linear Equations

scholarly journals On the numerical schemes for Langevin-type equations

2020 ◽  
Vol 99 (3) ◽  
pp. 62-74
Author(s):  
M. Akat ◽  
◽  
R. Kosker ◽  
A. Sirma ◽  
◽  
...  
Keyword(s):  
Numerical Scheme ◽  
Numerical Approach ◽  
Linear Case ◽  
Numerical Implementation ◽  
Numerical Schemes ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Non Linear ◽  
Numerical Discretization ◽  
The Stability

In this paper, a numerical approach is proposed based on the variation-of-constants formula for the numerical discretization Langevin-type equations. Linear and non-linear cases are treated separately. The proofs of convergence have been provided for the linear case, and the numerical implementation has been executed for the non-linear case. The order one convergence for the numerical scheme has been shown both theoretically and numerically. The stability of the numerical scheme has been shown numerically and depicted graphically.

B. The Non-Linear Calculations for Pulsating Stars

1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy
Keyword(s):  
Major Part ◽  
Afternoon Session ◽  
Discussion Session ◽  
Pulsating Stars ◽  
Fourth Symposium ◽  
Non Linear ◽  
Considerable Discussion ◽  
Informal Approach ◽  
Preceding Session

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)

A decomposition method in non-linear programmm

Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér
Keyword(s):  
Decomposition Method ◽  
Non Linear
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