The Numerical Solution of an Inverse Problem for a Class of One-Dimensional Diffusion Equations with Piecewise Constant Coefficients

1992 ◽  
Vol 52 (2) ◽  
pp. 428-441 ◽  
Author(s):  
Claudia Giordana ◽  
Marina Mochi ◽  
Francesco Zirilli
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Diffusion Equations ◽  
Piecewise Constant ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Constant Coefficients

Numerical Solution of the Differential Diffusion Equation for a Steel Carburizing Process

2018 ◽  
Vol 284 ◽  
pp. 1230-1234
Author(s):  
Mikhail V. Maisuradze ◽  
Alexandra A. Kuklina
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Differential Diffusion ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Diffusion ◽  
Simplified Algorithm ◽  
The One ◽  
Carburizing Process ◽  
Precise Assessment

The simplified algorithm of the numerical solution of the differential diffusion equation is presented. The solution is based on the one-dimensional diffusion model with the third kind boundary conditions and the finite difference method. The proposed approach allows for the quick and precise assessment of the carburizing process parameters – temperature and time.

On the solution of the Fokker–Planck equation for a Feller process

1990 ◽  
Vol 22 (01) ◽  
pp. 101-110
Author(s):  
L. Sacerdote
Keyword(s):  
Diffusion Processes ◽  
Planck Equation ◽  
Hyperbolic Type ◽  
Diffusion Equations ◽  
Time Varying ◽  
Feller Process ◽  
Parameter Group ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Type Boundary

Use of one-parameter group transformations is made to obtain the transition p.d.f. of a Feller process confined between the origin and a hyperbolic-type boundary. Such a procedure, previously used by Bluman and Cole (cf., for instance, [4]), although useful for dealing with one-dimensional diffusion processes restricted between time-varying boundaries, does not appear to have been sufficiently exploited to obtain solutions to the diffusion equations associated to continuous Markov processes.

scholarly journals Immersed Interface CIP for One Dimensional Hyperbolic Equations

2014 ◽  
Vol 16 (1) ◽  
pp. 96-114
Author(s):  
Kazufumi Ito ◽  
Tomoya Takeuchi
Keyword(s):  
Hyperbolic Equations ◽  
Third Order ◽  
Immersed Interface ◽  
Order Of Accuracy ◽  
Piecewise Constant ◽  
One Dimensional ◽  
The Third ◽  
Numerical Tests ◽  
Jump Discontinuities ◽  
Constant Coefficients

AbstractThe immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients. The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities, which is the same order of accuracy of the standard CIP scheme. Some numerical tests are given to verify the accuracy of the proposed method.

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