scholarly journals On the convergence of approximate solutions of the heat equation to the exact solution

1951 ◽  
Vol 2 (3) ◽  
pp. 433-433 ◽  
Author(s):  
Werner Leutert
Keyword(s):  
Exact Solution ◽  
Heat Equation ◽  
Approximate Solutions ◽  
Convergence Of Approximate Solutions

THE STRONG-NORM CONVERGENCE OF A PROJECTION-DIFFERENCE METHOD OF SOLUTION OF A PARABOLIC EQUATION WITH THE PERIODIC CONDITION ON THE SOLUTION

2018 ◽  
pp. 617-623
Author(s):  
Andrei Sergeevich Bondarev
Keyword(s):  
Exact Solution ◽  
Parabolic Equation ◽  
Difference Method ◽  
Approximate Solutions ◽  
Linear Parabolic Equation ◽  
Periodic Condition ◽  
Method Of Solution ◽  
The Galerkin Method ◽  
Convergence Of Approximate Solutions ◽  
Strong Norm

A smooth soluble abstract linear parabolic equation with the periodic condition on the solution is treated in a separable Hilbert space. This problem is solved approximately by a projection-difference method using the Galerkin method in space and the implicit Euler scheme in time. Effective both in time and in space strong-norm error estimates for approximate solutions, which imply convergence of approximate solutions to the exact solution and order of convergence rate depending of the smoothness of the exact solution, are obtained.

scholarly journals Model of an electro-rheological shock absorber and coupled problem for partial and ordinary differential equations with variable unknown domain

2007 ◽  
Vol 18 (4) ◽  
pp. 513-536 ◽  
Author(s):  
W. G. LITVINOV ◽  
T. RAHMAN ◽  
R. H. W. HOPPE
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Shock Absorber ◽  
Linear Equations ◽  
Approximate Solutions ◽  
Electrorheological Fluid ◽  
Coupled Problem ◽  
Uniqueness Of The Solution ◽  
Convergence Of Approximate Solutions ◽  
Non Linear Equations

Amortization of a shock in an electro-rheological shock absorber is carried out in the motion of a piston in an electrorheological fluid. The drag force acting on the piston is regulated by varying the voltage applied to electrodes. A model of an electrorheological shock absorber is constructed. A problem on shock absorber reduces to the solution of a coupled problem for motion equation of the piston and non-linear equations of fluid flow in an unknown domain that varies with the time. A method of semi-discretization for approximate solution of the coupled problem is considered. Results on the existence and on the uniqueness of the solution of the coupled problem are obtained. Convergence of approximate solutions to the exact solution is proved. Numerical simulation of the operation of the shock absorber is performed.

scholarly journals A perturbed algorithm for strongly nonlinear variational-like inclusions

2000 ◽  
Vol 62 (3) ◽  
pp. 417-426 ◽  
Author(s):  
C.-H. Lee ◽  
Q. H. Ansari ◽  
J.-C. Yao
Keyword(s):  
Exact Solution ◽  
General Setting ◽  
Approximate Solutions ◽  
Strongly Nonlinear ◽  
Special Cases ◽  
The One

In this paper, we define the concept of η- subdifferential in a more general setting than the one used by Yang and Craven in 1991. By using η-subdifferentiability, we suggest a perturbed algorithm for finding the approximate solutions of strongly nonlinear variational-like inclusions and prove that these approximate solutions converge to the exact solution. Several special cases are also discussed.

scholarly journals Satisfying positivity requirement in the Beyond Complex Langevin approach

2018 ◽  
Vol 175 ◽  
pp. 11026 ◽  
Author(s):  
Adam Wyrzykowski ◽  
Błażej Ruba Ruba
Keyword(s):  
Exact Solution ◽  
Approximate Solutions ◽  
Groebner Basis ◽  
Matching Conditions ◽  
Quadratic Equations ◽  
Positive Distribution ◽  
Langevin Approach ◽  
Basis Method ◽  
Special Case ◽  
Complex Density

The problem of finding a positive distribution, which corresponds to a given complex density, is studied. By the requirement that the moments of the positive distribution and of the complex density are equal, one can reduce the problem to solving the matching conditions. These conditions are a set of quadratic equations, thus Groebner basis method was used to find its solutions when it is restricted to a few lowest-order moments. For a Gaussian complex density, these approximate solutions are compared with the exact solution, that is known in this special case.

Sign in / Sign up

Export Citation Format

Share Document