scholarly journals A study of self-oscillation instability in varicap-based electrical networks: analytical and numerical approaches

2019 ◽  
pp. 323-336
Author(s):  
В.А. Васильченко ◽  
М.О. Корпусов ◽  
Д.В. Лукьяненко ◽  
А.А. Панин
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Analysis ◽  
Analytical Study ◽  
Complex Coefficient ◽  
A Posteriori ◽  
Electrical Networks ◽  
Blowup Of Solutions ◽  
Oscillation Instability ◽  
Numerical Approaches

Проведено аналитическое и численное исследование разрушения решения одного нелинейного уравнения cоболевского типа, которое описывает процессы в электрических схемах на основе варикапов. Аналитическое исследование проводилось энергетическим методом. Для численного решения исходное уравнение в частных производных аппроксимировалось с помощью метода прямых системой обыкновенных дифференциальных уравнений, которая затем решалась с помощью одностадийной схемы Розенброка с комплексным коэффициентом. В основе численной диагностики разрушения решения исследуемого уравнения лежало вычисление апостериорной асимптотически точной оценки погрешности приближенного решения на последовательно сгущающихся сетках. The blowup of solutions is analytically and numerically studied for a certain Sobolevtype equation describing processes in varicapbased electrical networks. The energy method is used for the analytical study. For the numerical analysis, the original partial differential equation is approximated using a system of ordinary differential equations solved by the onestage Rosenbrock scheme with a complex coefficient. The numerical diagnostics of solutions blowup is based on a posteriori asymptotically exact error estimation on sequentially condensed grids.

Numerical analysis of the convection and diffusion of solutes to roots

Soil Research ◽  
1967 ◽  
Vol 5 (2) ◽  
pp. 149 ◽  
Author(s):  
JB Passioura ◽  
MH Frere
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Medium ◽  
Diffusion Coefficient ◽  
Numerical Analysis ◽  
Average Concentration ◽  
Soil System ◽  
Dry Soil ◽  
The One ◽  
And Diffusion

A numerical method is given for solving a partial differential equation describing the radial movement of solutes through a porous medium to a root. Computer programmes based on the method were prepared and used to obtain solutions of the equation for an idealized root-soil system in which a solute is transported to the root by convection but is not taken up by the root. Various patterns of water uptake were considered, the most complex being a diurnally varying uptake from soil in which the water content is decreasing. The solutions suggest that the maximum build-up of solute at the surface of a root is trivial if the root is growing in a medium such as agar, in which the diffusion coefficient of the solute is high, but may be considerable, with a concentration up to 10 times higher than the average concentration in the soil solution, when the root is growing in a fairly dry soil. The application of the method to systems other than the one considered in detail is discussed.

NUMERICAL ANALYSIS OF MICRO–MACRO SIMULATIONS OF POLYMERIC FLUID FLOWS: A SIMPLE CASE

2002 ◽  
Vol 12 (09) ◽  
pp. 1205-1243 ◽  
Author(s):  
BENJAMIN JOURDAIN ◽  
TONY LELIÈVRE ◽  
CLAUDE LE BRIS
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Monte Carlo ◽  
Numerical Analysis ◽  
Test Problem ◽  
Fluid Flows ◽  
Equation System ◽  
Differential Equation System ◽  
Polymeric Fluid ◽  
Coupled Solution

We present in this paper the numerical analysis of a simple micro–macro simulation of a polymeric fluid flow, namely the shear flow for the Hookean dumbbells model. Although restricted to this academic case (which is however used in practice as a test problem for new numerical strategies to be applied to more sophisticated cases), our study can be considered as a first step towards that of more complicated models. Our main result states the convergence of the fully discretized scheme (finite element in space, finite difference in time, plus Monte Carlo realizations) towards the coupled solution of a partial differential equation/stochastic differential equation system.

Numerical Analysis of the Exact Solution of the Wave Equation of the Longitudinal Seismic Oscillations of Soil and the Construction as a Point Insertion

2018 ◽  
Vol 931 ◽  
pp. 152-157 ◽  
Author(s):  
Kamil D. Yaxubayev ◽  
Dinara D. Kochergina
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solution ◽  
Wave Equation ◽  
Numerical Analysis ◽  
Differential Equations ◽  
Partial Differential ◽  
Seismic Oscillations

The numerical analysis of the exact solution of the system of the differential equations which includes the partial differential equation of the longitudinal seismic oscillations of the soil and the ordinary differential equation of oscillations of the construction in the form of a point rigid insertion.

scholarly journals An Efficient Method for Solving Spread Option Pricing Problem: Numerical Analysis and Computing

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
R. Company ◽  
V. N. Egorova ◽  
L. Jódar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Analysis ◽  
Option Pricing ◽  
Computational Time ◽  
Explicit Difference Scheme ◽  
Spatial Variables ◽  
One Dimensional ◽  
Spread Option ◽  
The One

This paper deals with numerical analysis and computing of spread option pricing problem described by a two-spatial variables partial differential equation. Both European and American cases are treated. Taking advantage of a cross derivative removing technique, an explicit difference scheme is developed retaining the benefits of the one-dimensional finite difference method, preserving positivity, accuracy, and computational time efficiency. Numerical results illustrate the interest of the approach.

scholarly journals Behavior of the solutions of a partial differential equation with a piecewise constant argument

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5931-5943 ◽  
Author(s):  
Huseyin Bereketoglu ◽  
Mehtap Lafci
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Existence And Uniqueness ◽  
Partial Differential ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Oscillation Instability ◽  
Constant Argument

In this paper, we consider a partial differential equation with a piecewise constant argument. We study existence and uniqueness of the solutions of this equation. We also investigate oscillation, instability and stability of the solutions.

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