Numerical Method to Solve the Cauchy Problem with Previous History

2017 ◽  
Vol 53 (1) ◽  
pp. 34-56 ◽  
Author(s):  
V. A. Prusov ◽  
A. Yu. Doroshenko
Keyword(s):  
Cauchy Problem ◽  
Numerical Method ◽  
Previous History ◽  
The Cauchy Problem

scholarly journals An Integral Equations Method for the Cauchy Problem Connected with the Helmholtz Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yao Sun ◽  
Deyue Zhang
Keyword(s):  
Cauchy Problem ◽  
Approximate Solution ◽  
Helmholtz Equation ◽  
Numerical Method ◽  
Integral Equations ◽  
Regularization Method ◽  
Numerical Experiments ◽  
Suitable Choice ◽  
Convergence And Stability ◽  
The Cauchy Problem

We are concerned with the Cauchy problem connected with the Helmholtz equation. We propose a numerical method, which is based on the Helmholtz representation, for obtaining an approximate solution to the problem, and then we analyze the convergence and stability with a suitable choice of regularization method. Numerical experiments are also presented to show the effectiveness of our method.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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