Numerical methods for stiff systems of differential equations related with transistors, tunnel diodes, etc

2005 ◽  
pp. 416-432 ◽  
Author(s):  
Willard L. Miranker ◽  
Frank Hoppensteadt
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Tunnel Diodes ◽  
Stiff Systems ◽  
Systems Of Differential Equations

scholarly journals An Adaptation of the Scheifele Method to Stiff Systems of Differential Equations

2008 ◽  
Vol 2 (1) ◽  
pp. 86-94
Author(s):  
J. A. Reyes ◽  
F. Garcia-Alonso ◽  
Y. Villacampa
Keyword(s):  
Differential Equations ◽  
Stiff Systems ◽  
Systems Of Differential Equations

scholarly journals Effective numerical methods to model dynamic behavior of springs with torsion

2018 ◽  
Author(s):  
◽  
E. Dilan Fernando
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Method ◽  
Dynamic Behavior ◽  
Numerical Models ◽  
Software Implementation ◽  
Computer Language ◽  
Newtonian Mechanics ◽  
Systems Of Differential Equations ◽  
Kirchhoff Problem

The purpose of this thesis is to find effective algorithms to numerically solve certain systems of differential equations that arise from standard Newtonian mechanics. Numerical models of elastica has already been well studied. In this thesis we concentrate on the Kirchhoff problem. The goal is to create an effective and robust numerical method to model the dynamic behavior of springs that have a prescribed natural curvature. In addition to the mathematics, we also provide the implementation details of the numerical method using the computer language Python 3. We also discuss in detail the various difficulties of such a software implementation and how certain auxiliary computations can make the software more effective and robust.

scholarly journals Comparison of Numerical Methods for Solving Initial Value Problems for Stiff Differential Equations

1970 ◽  
Vol 30 ◽  
pp. 122-132
Author(s):  
Sharaban Thohura ◽  
Azad Rahman
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Procedure ◽  
Stiff Systems ◽  
Stiff Differential Equations ◽  
Initial Value ◽  
Step Size ◽  
Stepsize Control ◽  
Adaptive Stepsize ◽  
Runge Kutta

Special classes of Initial value problem of differential equations termed as stiff differential equations occur naturally in a wide variety of applications including the studies of spring and damping systems, chemical kinetics, electrical circuits, and so on. Most realistic stiff systems do not have analytical solutions so that a numerical procedure must be used. In this paper we have discussed the phenomenon of stiffness and the general purpose procedures for the solution of stiff differential equation. Because of their applications in many branches of engineering and science, many algorithms have been proposed to solve such problems. In this study we have focused on some conventional methods namely Runge-Kutta method, Adaptive Stepsize Control for Runge-Kutta and an ODE Solver package, EPISODE. We describe the characteristics shared by these methods. We compare the performance and the computational effort of such methods. In order to achieve higher accuracy in the solution, the traditional numerical methods such as Euler, explicit Runge-Kutta and Adams –Moulton methods step size need to be very small. This however introduces enough round-off errors to cause instability of the solution. To overcome this problem we have used two other algorithms namely Adaptive Stepsize Control for Runge-Kutta and EPISODE. The results are compared with exact one to determine the efficiency of the above mentioned method. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 121-132  DOI: http://dx.doi.org/10.3329/ganit.v30i0.8509

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