Numerical Solution of the Inverse Problem of Self-Diffusion

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

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A technique for calibrating derivative security pricing models: numerical solution of an inverse problem

The Journal of Computational Finance ◽

10.21314/jcf.1997.002 ◽

1997 ◽

Vol 1 (1) ◽

pp. 14-25 ◽

Cited By ~ 58

Author(s):

Ronald Lagnado ◽

Stanley Osher

Keyword(s):

Inverse Problem ◽

Numerical Solution ◽

Pricing Models ◽

Security Pricing

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The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.380-384.1143 ◽

2013 ◽

Vol 380-384 ◽

pp. 1143-1146

Author(s):

Xiang Guo Liu

Keyword(s):

Inverse Problem ◽

Diffusion Equation ◽

Perturbation Method ◽

Numerical Simulations ◽

Numerical Solution ◽

Two Dimensional ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

Parameter Inversion ◽

Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

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Numerical solution of inverse problem for secretion and kinetics of C-peptide model

2015 International Conference on Biomedical Engineering and Computational Technologies (SIBIRCON) ◽

10.1109/sibircon.2015.7361862 ◽

2015 ◽

Author(s):

S. I. Kabanikhin ◽

D. A. Voronov ◽

O. I. Krivorotko ◽

A. Yu. Belonog ◽

A. I. Ilyin

Keyword(s):

Inverse Problem ◽

Numerical Solution ◽

C Peptide ◽

Kinetics Of

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

Bulletin Series of Physics & Mathematical Sciences ◽

10.51889/2020-1.1728-7901.17 ◽

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.

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