The Cauchy problem for matrix factorization of the Helmholtz equation in a multidimensional unbounded domain

Juraev, Davron Aslonqulovich

doi:10.5269/bspm.63779

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2024

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Cited by 2 publications

References 15 publications

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The Cauchy problem for matrix factorizations of Helmholtz equation in space

Juraev,

Agarwal,

Shokri

et al. 2024

Recent Trends in Fractional Calculus and Its Applications

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The Cauchy problem for matrix factorizations of Helmholtz equation in space

Juraev,

Agarwal,

Shokri

et al. 2024

Recent Trends in Fractional Calculus and Its Applications

View full text Add to dashboard Cite

On Some Ways to Increase the Exactness of the Calculating Values of the Required Solutions for Some Mathematical Problems

Imanova,

Ibrahimov

2024

Wseas Transactions on Mathematics

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The expansion of the application of computational methods for solving many mathematical problems from various fields of natural knowledge does not raise any doubts. One of the promising directions in contemporary sciences is considered to be in areas that are at the intersection of different sciences. Solving such problems is more difficult because different laws from different areas are used. It should be noted that at the intersection of these sciences, there are problems, which can come down to solving ordinary differential equations. Therefore, studies of differential equations have always been considered promising. Based on this, the application of some methods for solving initial problems for first-order ODEs is investigated. For this purpose, scientists studied a numerical solution to the initial problem of the ODE. Here, we have reviewed the study of linear Multistep Methods with constant coefficients. With its help, the order of accuracy of the calculated values is determined. In addition, determines how much accuracy values increase when using Richardson extrapolation methods and also when using linear combinations of various methods. To construct an innovative method is proposed here using advanced methods. It is shown that using these methods it is possible that A-stable methods can be taken as innovative.

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The Cauchy problem for matrix factorization of the Helmholtz equation in a multidimensional unbounded domain

Abstract: In the present paper, a Carleman matrix is constructed and, on the basis of this matrix, an approximate solution of the Cauchy problem in a multidimensional unbounded domain is found in an explicit form.

Cited by 2 publications

References 15 publications

The Cauchy problem for matrix factorizations of Helmholtz equation in space

The Cauchy problem for matrix factorizations of Helmholtz equation in space

On Some Ways to Increase the Exactness of the Calculating Values of the Required Solutions for Some Mathematical Problems

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