Factorization of a convolution-type integro-differential equation on the positive half line

Khachatryan, A. Kh.; Khachatryan, Kh. A.

doi:10.1007/s11253-009-0172-6

Cited by 5 publications

(7 citation statements)

References 1 publication

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“…Multiplying by Ψ(G 0 ) from the left the second column of the matrix in (16) and then adding to the first column, we get…”

Section: Resultsmentioning

confidence: 99%

“…Boundary value problems involving an integro-differential equation and nonlocal boundary conditions are very difficult to solve analytically and therefore very often numerical methods are employed. Factorization methods, where they can be applied, can reduce the problem to simpler lower order problems which can be solved and thus construct the solution of the initial complex problem [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Factorization method for solving nonlocal boundary value problems in Banach space

Parasidis¹,

Providas²

2021

Bul. Kar. Univ. - Math.

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This article deals with the factorization and solution of nonlocal boundary value problems in a Banach space of the abstract form B1u = Au − SΦ(u) − GΨ(A0u) = f, u ∈ D(B1),where A, A0 are linear abstract operators, S, G are vectors of functions, Φ, Ψ are vectors of linear bounded functionals, and u, f are functions. It is shown that the operator B1 under certain conditions can be factorized into a product of two simpler lower order operators as B1 = BB0. Then the solvability and the unique solution of the equation B1u = f easily follow from the solvability conditions and the unique solutions of the equations Bv = f and B0u = v. The universal technique proposed here is essentially different from other factorization methods in the respect that it involves decomposition of both the equation and boundary conditions and delivers the solution in closed form. The method is implemented to solve ordinary and partial Fredholm integro-differential equations.

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“…Multiplying by Ψ(G 0 ) from the left the second column of the matrix in (16) and then adding to the first column, we get…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Factorization method for solving nonlocal boundary value problems in Banach space

Parasidis¹,

Providas²

2021

Bul. Kar. Univ. - Math.

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“…The most popular is Adomyan decomposition method and its modifications, where the Adomyan polynomials are used, and approximate solutions of given BVPs are obtained [11][12][13][14][15][16][17][18][19]. Other types of decomposition method were considered in [4], [5], [20]. Factorization of tensor integro-differential wave equations of the acoustics of dispersive viscoelastic anisotropic media is performed for the one-dimensional case in [4].…”

Section: Introductionmentioning

confidence: 99%

Factorization of abstract operators into two second degree operators and its applications to integro-differential equations

Parasidis,

Providas

2024

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Boundary value problem B1x = f with an abstract linear operator B1, corresponding to an Fredholm integro-differential equation with ordinary or partial differential operator is researched. An exact solution to B1x = f in the case when a bijective operator B1 has a factorization of the form B1 =BB0 where B and B0 are two linear more simple than B1 second degree abstract operators, received. Conditions for factorization of the operator B1 and a criterion for bijectivity of B1 are found.

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“…At first and after having to present the method, we propose to use the causal bond graph model of a lowpass filter based on Microstrip lines (distributed elements) (Trabelsi et al, 2003) to find, on the one hand, the integro-differentials operators (Khachatryan and Khachatryan, 2008) which based on the causal ways and algebraic loops present in the causal bond graph model and, on the other hand, to extract the wave matrix (Magnusson, 2001) from these operators.…”

Section: Introductionmentioning

confidence: 99%

Modeling Method of a Low-Pass Filter Based on Microstrip T-Lines with Cut-Off Frequency 10 GHz by the Extraction of its Wave-Scattering Parameters from its Causal Bond Graph Model

Taghouti¹,

Mami²

2010

American J. of Engineering and Applied Sciences

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Problem statement: This study presented a jointly application of bond graph technique and wave-scattering formalism for a new realization called scattering bond graph model which has the main advantage to show up explicitly the different wave propagation. Approach: For that, we proposed to find the scattering matrix from the causal bond graph model of a low-pass filter based on Microstrip lines and with cut-off frequency 10 GHz, while starting with determination of the integro-differentials operators which is based, in their determination, on the causal ways and causal algebraic loops present in the associated bond graph model and which gives rise to the wave matrix which gathers the incident and reflected waves propagation of the studied filter. Results: The scattering parameters, founded from the wave matrix, will be checked by comparison of the simulation results. Conclusion: Thereafter, we use a procedure to model directly this scattering matrix under a special bond graph model form often called Scattering Bond Graph Model

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Factorization of a convolution-type integro-differential equation on the positive half line

Abstract: 517.9Sufficient conditions for the existence of solutions are obtained for a class of convolution-type integro-differential equations on the half line. The investigation is based on the three-factor decomposition of the initial integro-differential operator.

Cited by 5 publications

References 1 publication

Factorization method for solving nonlocal boundary value problems in Banach space

Factorization method for solving nonlocal boundary value problems in Banach space

Factorization of abstract operators into two second degree operators and its applications to integro-differential equations

Modeling Method of a Low-Pass Filter Based on Microstrip T-Lines with Cut-Off Frequency 10 GHz by the Extraction of its Wave-Scattering Parameters from its Causal Bond Graph Model

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