Numerical Solution of Nonlinear Differential Equations with Algebraic Constraints II: Practical Implications

1986 ◽  
Vol 7 (3) ◽  
pp. 720-733 ◽  
Author(s):  
Linda Petzold ◽  
Per Lötstedt
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Nonlinear Differential Equations ◽  
Algebraic Constraints ◽  
Practical Implications

NUMERICAL SOLUTION OF THE INVERSE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 106-110
Author(s):  
S.E. Kasenov ◽  
◽  
G.E. Kasenova ◽  
A.A. Sultangazin ◽  
B.D. Bakytbekova ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Numerical Solution ◽  
Direct Problem ◽  
Nonlinear Differential Equations ◽  
Direct And Inverse Problems ◽  
Additional Information ◽  
Several Variables ◽  
Gradient Of The Functional ◽  
Objective Functional

The article considers direct and inverse problems of a system of nonlinear differential equations. Such problems are often found in various fields of science, especially in medicine, chemistry and economics. One of the main methods for solving nonlinear differential equations is the numerical method. The initial direct problem is solved by the Rune-Kutta method with second accuracy and graphs of the numerical solution are shown. The inverse problem of finding the coefficients of a system of nonlinear differential equations with additional information on solving the direct problem is posed. The numerical solution of this inverse problem is reduced to minimizing the objective functional. One of the methods that is applicable to nonsmooth and noisy functionals, unconditional optimization of the functional of several variables, which does not use the gradient of the functional, is the Nelder-Mead method. The article presents the NellerMead algorithm. And also a numerical solution of the inverse problem is shown.

scholarly journals Destroying synchrony in an array of the FitzHugh–Nagumo oscillators by external DC voltage source

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Elena Adomaitienė ◽  
Skaidra Bumelienė ◽  
Gytis Mykolaitis ◽  
Arūnas Tamaševičius
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Control Method ◽  
Nonlinear Differential Equations ◽  
Mean Field ◽  
Electrical Circuit ◽  
Voltage Source ◽  
Dc Voltage

A control method for desynchronizing an array of mean-field coupled FitzHugh–Nagumo-type oscillators is described. The technique is based on applying an adjustable DC voltage source to the coupling node. Both, numerical solution of corresponding nonlinear differential equations and hardware experiments with a nonlinear electrical circuit have been performed.

Haar wavelet based numerical solution of nonlinear differential equations arising in fluid dynamics

2016 ◽  
Vol 05 (02) ◽  
pp. 1650010 ◽  
Author(s):  
S. C. Shiralashetti ◽  
M. H. Kantli ◽  
A. B. Deshi
Keyword(s):  
Fluid Dynamics ◽  
Differential Equations ◽  
Error Analysis ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Elastohydrodynamic Lubrication ◽  
Haar Wavelet ◽  
Nonlinear Boundary Value Problems

In this paper, we obtained the Haar wavelet-based numerical solution of the nonlinear differential equations arising in fluid dynamics, i.e., electrohydrodynamic flow, elastohydrodynamic lubrication and nonlinear boundary value problems. Error analysis is observed, it shows that the Haar wavelet-based results give better accuracy than the existing methods, which is justified through illustrative examples.

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