Boundary regularized integral equation formulation of the Helmholtz equation in acoustics [PDF]
Royal Society Open Science, 2015 A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically.
Qiang Sun +3 more
doaj +5 more sources
Boundary value problem for the heat equation with a load as the Riemann-Liouville fractional derivative [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 A boundary value problem for a fractionally loaded heat equation is considered in the first quadrant. The loaded term has the form of the Riemann-Liouville’s fractional derivative with respect to the time variable, and the order of the ...
A.V. Pskhu +4 more
doaj +3 more sources
Unique solvability of boundary value problem for functional differential equations with involution [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 In this paper we consider a boundary value problem for systems of Fredholm type integral-differential equations with involutive transformation, containing derivative of the required function on the right-hand side under the integral sign ...
K.Zh. Nazarova, K.I. Usmanov
doaj +3 more sources
Analysis of Two-Dimensional Heat Transfer Problem Using the Boundary Integral Equation
Advances in Mathematical Physics, 2022 In this paper, we examine the problem of two-dimensional heat equations with certain initial and boundary conditions being considered. In a two-dimensional heat transport problem, the boundary integral equation technique was applied.
Nimona Ketema Kebeba, Gizaw Debito Haifo
doaj +1 more source
Mathematical Modelling and Analysis, 2022 The time-dependent Laplace-type equation of variable coefficients for anisotropic inhomogeneous media is discussed in this paper. Numerical solutions to problems which are governed by the equation are sought by using a combined Laplace transform and ...
Mohammad Ivan Azis
doaj +1 more source
A Source Problem for the Helmholtz Equation via a Dirichlet-to-Neumann Map
Abstract and Applied Analysis, 2021 In this paper, we consider a source problem for a time harmonic acoustic wave in two-dimensional space. Based on the boundary integral equation method, a Dirichlet-to-Neumann map in terms of boundary integral operators on the boundary of the source is ...
Kuo-Ming Lee
doaj +1 more source
To solving the fractionally loaded heat equation
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 In this paper we consider a boundary value problem for a fractionally loaded heat equation in the class of continuous functions. Research methods are based on an approach to the study of boundary value problems, based on their reduction to integral ...
M.T. Kosmakova +2 more
doaj +1 more source
SOLUTION OF A TWO-DIMENSIONAL BOUNDARY VALUE PROBLEM OF HEAT CONDUCTION IN A DEGENERATING DOMAIN
Вестник КазНУ. Серия математика, механика, информатика, 2021 In the paper we consider the boundary value problem of heat conduction outside the cone, i.e. in the domain degenerating into a point at the initial moment of time.
M. I. Ramazanov +1 more
doaj +1 more source
On the uniqueness of linear convection–diffusion equations with integral boundary conditions
Comptes Rendus. Mathématique, 2023 We investigate a class of convection–diffusion equations in an expanding domain involving a parameter, where we consider integral boundary conditions that depend non-locally on unknown solutions.
Lee, Chiun-Chang +2 more
doaj +1 more source
Asymptotic analysis of Sturm–Liouville problem with nonlocal integral-type boundary condition
Nonlinear Analysis, 2021 In this study, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the one-dimensional Sturm–Liouville equation with one classical-type Dirichlet boundary condition and integral-type nonlocal boundary condition.
Artūras Štikonas, Erdoğan Şen
doaj +1 more source