Differential-symbol method of constructing the quasipolynomial solutions of a two-point problem for a partial differential equation

Nytrebych, Zinovii; Ільків, В. С.; Пукач, Петро; Маланчук, Оксана

doi:10.1007/s10958-019-04288-9

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Introduction2

The Polynomial Solution Of the Inhomogeneous Helmholtz Equation1

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2020

2021

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Cited by 2 publications

(3 citation statements)

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“…Applying the inverse Fourier transform, we obtain the unique solution of the Dirichlet problem (8), (9) in the class of functions of slow growth in the form of convolution…”

Section: The Polynomial Solution Of the Inhomogeneous Helmholtz Equationmentioning

confidence: 99%

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Exact Solutions to the Boundary-Value Problems for the Helmholtz Equation in a Layer With Polynomials in the Right-Hand Sides of the Equation and of the Boundary Conditions

Algazin

2020

Bulletin of the MSRU (Physics and Mathematics)

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In a multidimensional infinite layer bounded by two hyperplanes, the inhomogeneous Helmholtz equation with a polynomial right-hand side is considered. It is shown that the Dirichlet and Dirichlet-Neumann boundaryvalue problems with polynomials in the right-hand sides of the boundary conditions have a solution that is a quasipolynomial that contains, in addition to the power functions, also hyperbolic or trigonometric functions. This solution is unique in the class of slow growth functions if the parameter of the equation is not an eigenvalue. An algorithm for constructing this solution is given and examples are considered.

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“…Applying the inverse Fourier transform, we obtain the unique solution of the Dirichlet problem (8), (9) in the class of functions of slow growth in the form of convolution…”

Section: The Polynomial Solution Of the Inhomogeneous Helmholtz Equationmentioning

confidence: 99%

“…In the same way, exact polynomial solutions of boundary value problems for the Tricomi equation in a strip are obtained [3], [4]. The search for solutions of partial differential equations in the form of polynomials or quasipolynomials has been the subject of work by many authors [5] - [9].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions to the Boundary-Value Problems for the Helmholtz Equation in a Layer With Polynomials in the Right-Hand Sides of the Equation and of the Boundary Conditions

Algazin

2020

Bulletin of the MSRU (Physics and Mathematics)

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show abstract

“…Поиску решений уравнений с частными производными в виде полиномов или квазиполиномов посвящены работы многих авторов [8][9][10][11][12], см . также [13][14][15] .…”

Section: Introductionunclassified

Boundary Value Problems for the Poisson Equation in a Half-Space With Polynomial Data and the Cauchy Problem

Algazin

2021

Bulletin of the MSRU (Physics and Mathematics)

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Differential-symbol method of constructing the quasipolynomial solutions of a two-point problem for a partial differential equation

Cited by 2 publications

References 6 publications

Exact Solutions to the Boundary-Value Problems for the Helmholtz Equation in a Layer With Polynomials in the Right-Hand Sides of the Equation and of the Boundary Conditions

Exact Solutions to the Boundary-Value Problems for the Helmholtz Equation in a Layer With Polynomials in the Right-Hand Sides of the Equation and of the Boundary Conditions

Boundary Value Problems for the Poisson Equation in a Half-Space With Polynomial Data and the Cauchy Problem

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